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Some Results on 𝑫-Homothetic Deformations

Year 2018, Volume: 18 Issue: 3, 878 - 883, 30.12.2018

Abstract

The main goal of this article is to investigate the 𝐷-homothetic deformation of an almost alpha cosymplectic manifold. Some results on almost alpha cosymplectic manifolds using 𝐷-homothetic deformation are obtained. Finally, an illustrative example is given on such manifolds

References

  • Blair, D.E., 2002. Riemannian Geometry of Contact and Symplectic Manifolds, Progress in Mathematics, 203. Birkhâuser, Boston, USA.
  • Blair, D.E., Koufogiorgos T. and Papantoniou, B.J., 1995. Contact metric manifolds satisfying a nullity condition,. Israel J. Math., 91, 189-214
  • . Boeckx, E., 2000. A full classification of contact metric (𝜅,𝜇)-spaces, Illinois J. Math., 44(1), 212-219.
  • Carriazo, A. and Martin-Molina, V., 2011. Generalized (𝜅,𝜇)-space forms and 𝐷𝑎-homothetic deformations, Balkan Journal of Geometry and its applications, 16 (1), 37-47.
  • Dacko, P. and Olszak, Z., 2005. On almost cosymplectic (𝜅,𝜇,𝜈)-spaces, Banach Center Publ., 69, 211-220.
  • Dacko, P. and Olszak, Z., 2005. On almost cosymplectic (−1,𝜇,0)-spaces, Cent. Eur. J. Math., 3(2), 318-330.
  • De, U.C. and Ghosh, S., 2013. 𝐷-homothetic deformation of normal almost contact metric manifolds, Ukrainian Math. J., 65(10), 1330-1345
  • . Öztürk, H., Aktan, N., Murathan C. and Vanlı, A.T., 2014. Almost 𝛼-cosymplectic 𝑓-manifolds. The J. Alexandru Ioan Cuza Univ., 60, 211-226.
  • Öztürk, H., Mısırlı İ. and Öztürk, S., 2017. Almost alpha- Cosymplectic Manifolds with eta-parallel tensor fields, Academic Journal of Science, 7(3), 605-612.
  • Öztürk, H., 2016. On Almost α-Kenmotsu Manifolds with Some Tensor Fields, AKU J. Sci. Eng., 16(2), 256-264.
  • Kenmotsu, K., 1972. A class of contact Riemannian Some manifold, Tohoku Math. J., 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., 21(4), 841-846.
  • Montano, C.B. and Terlizzi, D.L., 2007. 𝐷-homothetic transformations for a generalized of contact metric manifolds, Bull. Belg. Math. Soc. Simon Steven, 14, 277-289.
  • Olszak, Z., 1989. Locally conformal almost cosymplectic manifolds, Coll. Math., 57, 73-87
  • . Tanno, S., 1968. The topology of contact Riemannian manifolds, Tohoku Math. J., 12, 700-712.
  • Vaisman, I., 1980. Conformal changes of almost contact metric manifolds, Lecture Notes in Math., Berlin-Heidelberg-New York, 792, 435-443.
  • Yano, K. and Kon, M., 1984. Structures on Manifolds, Series in Pure Math., 3. World Scientific Publishing, Singapore.
Year 2018, Volume: 18 Issue: 3, 878 - 883, 30.12.2018

Abstract

References

  • Blair, D.E., 2002. Riemannian Geometry of Contact and Symplectic Manifolds, Progress in Mathematics, 203. Birkhâuser, Boston, USA.
  • Blair, D.E., Koufogiorgos T. and Papantoniou, B.J., 1995. Contact metric manifolds satisfying a nullity condition,. Israel J. Math., 91, 189-214
  • . Boeckx, E., 2000. A full classification of contact metric (𝜅,𝜇)-spaces, Illinois J. Math., 44(1), 212-219.
  • Carriazo, A. and Martin-Molina, V., 2011. Generalized (𝜅,𝜇)-space forms and 𝐷𝑎-homothetic deformations, Balkan Journal of Geometry and its applications, 16 (1), 37-47.
  • Dacko, P. and Olszak, Z., 2005. On almost cosymplectic (𝜅,𝜇,𝜈)-spaces, Banach Center Publ., 69, 211-220.
  • Dacko, P. and Olszak, Z., 2005. On almost cosymplectic (−1,𝜇,0)-spaces, Cent. Eur. J. Math., 3(2), 318-330.
  • De, U.C. and Ghosh, S., 2013. 𝐷-homothetic deformation of normal almost contact metric manifolds, Ukrainian Math. J., 65(10), 1330-1345
  • . Öztürk, H., Aktan, N., Murathan C. and Vanlı, A.T., 2014. Almost 𝛼-cosymplectic 𝑓-manifolds. The J. Alexandru Ioan Cuza Univ., 60, 211-226.
  • Öztürk, H., Mısırlı İ. and Öztürk, S., 2017. Almost alpha- Cosymplectic Manifolds with eta-parallel tensor fields, Academic Journal of Science, 7(3), 605-612.
  • Öztürk, H., 2016. On Almost α-Kenmotsu Manifolds with Some Tensor Fields, AKU J. Sci. Eng., 16(2), 256-264.
  • Kenmotsu, K., 1972. A class of contact Riemannian Some manifold, Tohoku Math. J., 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., 21(4), 841-846.
  • Montano, C.B. and Terlizzi, D.L., 2007. 𝐷-homothetic transformations for a generalized of contact metric manifolds, Bull. Belg. Math. Soc. Simon Steven, 14, 277-289.
  • Olszak, Z., 1989. Locally conformal almost cosymplectic manifolds, Coll. Math., 57, 73-87
  • . Tanno, S., 1968. The topology of contact Riemannian manifolds, Tohoku Math. J., 12, 700-712.
  • Vaisman, I., 1980. Conformal changes of almost contact metric manifolds, Lecture Notes in Math., Berlin-Heidelberg-New York, 792, 435-443.
  • Yano, K. and Kon, M., 1984. Structures on Manifolds, Series in Pure Math., 3. World Scientific Publishing, Singapore.
There are 17 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Hakan Öztürk

Sermin Öztürk

Publication Date December 30, 2018
Submission Date August 2, 2018
Published in Issue Year 2018 Volume: 18 Issue: 3

Cite

APA Öztürk, H., & Öztürk, S. (2018). Some Results on 𝑫-Homothetic Deformations. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 18(3), 878-883.
AMA Öztürk H, Öztürk S. Some Results on 𝑫-Homothetic Deformations. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. December 2018;18(3):878-883.
Chicago Öztürk, Hakan, and Sermin Öztürk. “Some Results on 𝑫-Homothetic Deformations”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 18, no. 3 (December 2018): 878-83.
EndNote Öztürk H, Öztürk S (December 1, 2018) Some Results on 𝑫-Homothetic Deformations. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 18 3 878–883.
IEEE H. Öztürk and S. Öztürk, “Some Results on 𝑫-Homothetic Deformations”, Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 18, no. 3, pp. 878–883, 2018.
ISNAD Öztürk, Hakan - Öztürk, Sermin. “Some Results on 𝑫-Homothetic Deformations”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 18/3 (December 2018), 878-883.
JAMA Öztürk H, Öztürk S. Some Results on 𝑫-Homothetic Deformations. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2018;18:878–883.
MLA Öztürk, Hakan and Sermin Öztürk. “Some Results on 𝑫-Homothetic Deformations”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 18, no. 3, 2018, pp. 878-83.
Vancouver Öztürk H, Öztürk S. Some Results on 𝑫-Homothetic Deformations. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2018;18(3):878-83.