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The Investigation of Some Tensor Conditions for α-Kenmotsu Pseudo-Metric Structures

Year 2022, Volume: 22 Issue: 6, 1314 - 1322, 28.12.2022
https://doi.org/10.35414/akufemubid.1169777

Abstract

This paper aims to study some semi-symmetric and curvature tensor conditions on α-Kenmotsu pseudo-metric manifolds. Some conditions of semi-symmetric, locally symmetric, and the Ricci semi-symmetric are considered on such manifolds. Also, the relationships between the M-projective curvature tensor and conformal curvature tensor, concircularly curvature tensor, and conharmonic curvature tensor are investigated. Finally, an example of α-Kenmotsu pseudo-metric structure is given.

Thanks

The author would like to thank the anonymous referee for the useful improvements suggested.

References

  • Bagewadi, C.S. and Venkatesha, V., 2007. Some curvature tensors on a trans-Sasakian manifold, Turkish J. Math., 31, 111–121.
  • Blair, D., 1976. Contact manifolds in Riemannian geometry, Lecture Notes in Math. Springer-Verlag, Berlin-Heidelberg, New York, USA.
  • Calvaruso, G. and Perrone, D., 2002. Semi-symmetric contact metric three-manifolds, Yokohama Math. J., 49, 149–161.
  • Calvaruso, G. and Perrone, D., 2010. Contact pseudo-metric manifolds. Differential Geometry and its Applications, 28, 615–634.
  • Calvaruso, G., 2011. Contact Lorentzian manifolds. Differential Geometry and its Applications, 29, 541–551.
  • Duggal, K.L., 1990. Space time manifolds and contact structures. Internat. J. Math. & Math. Sci, 13, 545–554.
  • Gray, J.W., 1959. Some global properties of contact structures, Annals of Mathematics Second Series, 69, 421–450.
  • Goldberg, S.I. and Yano, K., 1969. Integrability of almost cosymplectic structure, Pacific Journal Math., 31, 373–382.
  • Jun, J.B., De, U.C. and Pathak, G., 2005. On Kenmotsu manifolds, J. Korean Math. Soc., 42, 435–445.
  • Kenmotsu, K., 1972. A class of contact Riemannian manifold, Tôhoku Math. Journal, 24 , 93–103.
  • Kim, T.W. and Pak, H.K., 2005. Canonical foliations of certain Classes of almost contact metric structures, Acta Math. Sinica, Eng. Ser. Aug., 21, 841–846.
  • Naik, D.M., Venkatesha, V. and Kumara, H.A., 2020. Some results on almost Kenmotsu manifolds, Note Math., 40, 87–100.
  • Nomizu, K., 1968. On hypersurfaces satisfying a certain condition on the curvature tensor, Tôhoku Mat. J., 20, 46–69.
  • Ogawa, Y., 1977. A condition for a compact Kaehlerian space to be locally symmetric, Nat. Sci. Rep. Ochanomizu Univ., 28, 21–23.
  • O’Neil, B., 1983. Semi-Riemannian geometry with applications to relativity, Academic Press, New York.
  • Olszak, Z., 1981. On almost cosymplectic manifolds, Kodai Math, 4(2), 239–250.
  • Olszak, Z., 1989. Locally conformal almost cosymplectic manifolds, College Mathematical Journal, 57, 73–87.
  • Özgür, C., 2007. On generalized reccurent Kenmotsu manifolds, World Appl.Sci. J., 2, 9–33.
  • Öztürk, H., 2017. On α-Kenmotsu manifolds satisfying semi-symmetric conditions, Konuralp Journal of Mathematics, 5(2), 192–206.
  • Öztürk, H., Mısırlı, M. and Öztürk, S., 2017. Almost α-cosymplectic manifolds with η-parallel tensor fields, Academic Journal of Science, 7(3), 605–612.
  • Öztürk, H. and Öztürk, S., 2018. Some results on D-homothetic deformation, AKU Journal of Science and Eng., 18, 878–883.
  • Öztürk, H. and Öztürk S., 2018. On almost alpha Kenmotsu (k,μ)-spaces, Journal of Advances in Mathemetics, 14(2), 7905–7911.
  • Öztürk, S. and Öztürk H., 2020. On alpha Kenmotsu pseudo metric manifolds, AKU Journal of Science and Eng., 20, 975–982.
  • Öztürk, S. and Öztürk H., 2021. Almost α-cosymplectic pseudo metric manifolds, Journal of Mathematics, 2021, Article ID 4106025, 1–10.
  • Öztürk, S. and Öztürk H., 2021. Certain class of almost α-cosymplectic manifolds, Journal of Mathematics, 2021, Article ID 9277175, 1–9.
  • Pokhariyal, G.P. and Mishra R.S., 1971. Curvature tensor and their relativistic significance II, Yokohama Mathematical Journal, 19 , 97−103,
  • Sasaki, S., 1960. On differentiable manifolds with certain structures which are closely related to almost contact structures I, Tôhoku Math. Journal, 12, 459–476.
  • Sasaki, S. and Hatakeyama, Y., 1962. On differentiable manifolds with contact metric structures, Journal of the Mathematical Society of Japan, 14, 249–271.
  • Szabó, Z.I., 1982. Structure theorem on Riemannian spaces satisfying R.R=0, Journal of Differential Geo., 17, 531–582.
  • Perrone, D., 2014. Contact pseudo-metric manifolds of constant curvature and CR geometry, Results in Mathematics, 66, 213–225.
  • Takahashi, T., 1969. Sasakian manifold with pseudo-Riemannian manifolds, Tôhoku Math. Journal, 21, 271–290.
  • Yano, K. And Kon, M., 1984. Structures on manifolds, Series in Pure Mathematics, 3. World Scientific Publishing Co., Singapore.
  • Venkatesha, V. and Bagewadi, C.S., 2006. On pseudo projective φ-recurrent Kenmotsu manifolds, Sooch. J. Math., 32, 1–7.
  • Wang, Y. And Liu, X., 2016. Almost Kenmotsu pseudo-metric manifolds, Analele Stiintifice ale Universitatii Al I Cuza din Iasi - Matematica, 62, 241–256.

Bazı Tensör Koşullarının α-Kenmotsu Pseudo-Metrik Yapılar İçin İncelenmesi

Year 2022, Volume: 22 Issue: 6, 1314 - 1322, 28.12.2022
https://doi.org/10.35414/akufemubid.1169777

Abstract

Bu makale α-Kenmotsu pseudo-metrik manifoldlar üzerinde bazı yarı simetrik ve eğrilik tensör şartlarını çalışmayı amaçlamaktadır. Bazı yarı-simetrik, lokal simetrik ve Ricci yarı-simetrik şartlar bu tür manifoldlar için göz önüne alınmıştır. Ayrıca, M-projektif eğrilik tensörü ile konformal eğrilik tensörü, konsirküler eğrilik tensörü ve konharmonik eğrilik tensörü arasındaki ilişkiler araştırılmıştır. Makale açıklayıcı bir α-Kenmotsu pseudo-metrik manifold örneği ile sonlandırılmıştır.

References

  • Bagewadi, C.S. and Venkatesha, V., 2007. Some curvature tensors on a trans-Sasakian manifold, Turkish J. Math., 31, 111–121.
  • Blair, D., 1976. Contact manifolds in Riemannian geometry, Lecture Notes in Math. Springer-Verlag, Berlin-Heidelberg, New York, USA.
  • Calvaruso, G. and Perrone, D., 2002. Semi-symmetric contact metric three-manifolds, Yokohama Math. J., 49, 149–161.
  • Calvaruso, G. and Perrone, D., 2010. Contact pseudo-metric manifolds. Differential Geometry and its Applications, 28, 615–634.
  • Calvaruso, G., 2011. Contact Lorentzian manifolds. Differential Geometry and its Applications, 29, 541–551.
  • Duggal, K.L., 1990. Space time manifolds and contact structures. Internat. J. Math. & Math. Sci, 13, 545–554.
  • Gray, J.W., 1959. Some global properties of contact structures, Annals of Mathematics Second Series, 69, 421–450.
  • Goldberg, S.I. and Yano, K., 1969. Integrability of almost cosymplectic structure, Pacific Journal Math., 31, 373–382.
  • Jun, J.B., De, U.C. and Pathak, G., 2005. On Kenmotsu manifolds, J. Korean Math. Soc., 42, 435–445.
  • Kenmotsu, K., 1972. A class of contact Riemannian manifold, Tôhoku Math. Journal, 24 , 93–103.
  • Kim, T.W. and Pak, H.K., 2005. Canonical foliations of certain Classes of almost contact metric structures, Acta Math. Sinica, Eng. Ser. Aug., 21, 841–846.
  • Naik, D.M., Venkatesha, V. and Kumara, H.A., 2020. Some results on almost Kenmotsu manifolds, Note Math., 40, 87–100.
  • Nomizu, K., 1968. On hypersurfaces satisfying a certain condition on the curvature tensor, Tôhoku Mat. J., 20, 46–69.
  • Ogawa, Y., 1977. A condition for a compact Kaehlerian space to be locally symmetric, Nat. Sci. Rep. Ochanomizu Univ., 28, 21–23.
  • O’Neil, B., 1983. Semi-Riemannian geometry with applications to relativity, Academic Press, New York.
  • Olszak, Z., 1981. On almost cosymplectic manifolds, Kodai Math, 4(2), 239–250.
  • Olszak, Z., 1989. Locally conformal almost cosymplectic manifolds, College Mathematical Journal, 57, 73–87.
  • Özgür, C., 2007. On generalized reccurent Kenmotsu manifolds, World Appl.Sci. J., 2, 9–33.
  • Öztürk, H., 2017. On α-Kenmotsu manifolds satisfying semi-symmetric conditions, Konuralp Journal of Mathematics, 5(2), 192–206.
  • Öztürk, H., Mısırlı, M. and Öztürk, S., 2017. Almost α-cosymplectic manifolds with η-parallel tensor fields, Academic Journal of Science, 7(3), 605–612.
  • Öztürk, H. and Öztürk, S., 2018. Some results on D-homothetic deformation, AKU Journal of Science and Eng., 18, 878–883.
  • Öztürk, H. and Öztürk S., 2018. On almost alpha Kenmotsu (k,μ)-spaces, Journal of Advances in Mathemetics, 14(2), 7905–7911.
  • Öztürk, S. and Öztürk H., 2020. On alpha Kenmotsu pseudo metric manifolds, AKU Journal of Science and Eng., 20, 975–982.
  • Öztürk, S. and Öztürk H., 2021. Almost α-cosymplectic pseudo metric manifolds, Journal of Mathematics, 2021, Article ID 4106025, 1–10.
  • Öztürk, S. and Öztürk H., 2021. Certain class of almost α-cosymplectic manifolds, Journal of Mathematics, 2021, Article ID 9277175, 1–9.
  • Pokhariyal, G.P. and Mishra R.S., 1971. Curvature tensor and their relativistic significance II, Yokohama Mathematical Journal, 19 , 97−103,
  • Sasaki, S., 1960. On differentiable manifolds with certain structures which are closely related to almost contact structures I, Tôhoku Math. Journal, 12, 459–476.
  • Sasaki, S. and Hatakeyama, Y., 1962. On differentiable manifolds with contact metric structures, Journal of the Mathematical Society of Japan, 14, 249–271.
  • Szabó, Z.I., 1982. Structure theorem on Riemannian spaces satisfying R.R=0, Journal of Differential Geo., 17, 531–582.
  • Perrone, D., 2014. Contact pseudo-metric manifolds of constant curvature and CR geometry, Results in Mathematics, 66, 213–225.
  • Takahashi, T., 1969. Sasakian manifold with pseudo-Riemannian manifolds, Tôhoku Math. Journal, 21, 271–290.
  • Yano, K. And Kon, M., 1984. Structures on manifolds, Series in Pure Mathematics, 3. World Scientific Publishing Co., Singapore.
  • Venkatesha, V. and Bagewadi, C.S., 2006. On pseudo projective φ-recurrent Kenmotsu manifolds, Sooch. J. Math., 32, 1–7.
  • Wang, Y. And Liu, X., 2016. Almost Kenmotsu pseudo-metric manifolds, Analele Stiintifice ale Universitatii Al I Cuza din Iasi - Matematica, 62, 241–256.
There are 34 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Hakan Öztürk 0000-0003-1299-3153

Early Pub Date December 15, 2022
Publication Date December 28, 2022
Submission Date September 1, 2022
Published in Issue Year 2022 Volume: 22 Issue: 6

Cite

APA Öztürk, H. (2022). The Investigation of Some Tensor Conditions for α-Kenmotsu Pseudo-Metric Structures. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 22(6), 1314-1322. https://doi.org/10.35414/akufemubid.1169777
AMA Öztürk H. The Investigation of Some Tensor Conditions for α-Kenmotsu Pseudo-Metric Structures. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. December 2022;22(6):1314-1322. doi:10.35414/akufemubid.1169777
Chicago Öztürk, Hakan. “The Investigation of Some Tensor Conditions for α-Kenmotsu Pseudo-Metric Structures”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 22, no. 6 (December 2022): 1314-22. https://doi.org/10.35414/akufemubid.1169777.
EndNote Öztürk H (December 1, 2022) The Investigation of Some Tensor Conditions for α-Kenmotsu Pseudo-Metric Structures. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 22 6 1314–1322.
IEEE H. Öztürk, “The Investigation of Some Tensor Conditions for α-Kenmotsu Pseudo-Metric Structures”, Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 22, no. 6, pp. 1314–1322, 2022, doi: 10.35414/akufemubid.1169777.
ISNAD Öztürk, Hakan. “The Investigation of Some Tensor Conditions for α-Kenmotsu Pseudo-Metric Structures”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 22/6 (December 2022), 1314-1322. https://doi.org/10.35414/akufemubid.1169777.
JAMA Öztürk H. The Investigation of Some Tensor Conditions for α-Kenmotsu Pseudo-Metric Structures. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2022;22:1314–1322.
MLA Öztürk, Hakan. “The Investigation of Some Tensor Conditions for α-Kenmotsu Pseudo-Metric Structures”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 22, no. 6, 2022, pp. 1314-22, doi:10.35414/akufemubid.1169777.
Vancouver Öztürk H. The Investigation of Some Tensor Conditions for α-Kenmotsu Pseudo-Metric Structures. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2022;22(6):1314-22.