Research Article
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Year 2020, Volume: 3 Issue: 1, 57 - 66, 25.03.2020

Abstract

References

  • [1] S. Lie, Geometrie der Beruhrungstransformationen. B.G. Teubner, Leipzig, (1896).
  • [2] H. Geiges, An Introduction to Contact Topology. Cambridge University Press, New York (2008).
  • [3] H. Geiges, A brief history of contact geometry and topology. Expo. Math. 19(1), 25-53 (2001).
  • [4] H. Geiges, Christiaan Huygens and contact geometry. Nieuw Arch. Wiskd (5). 6(2), 117-123. (2005).
  • [5] A. Bejancu, CR-submanifolds of a Kaehler manifold-I, Proc. Amer. Math. Soc., 69(1978), 135-42.
  • [6] M. H. Shahid, A. Sharfuddin and S.I. Husain, CR-submanifolds of a Sasakian manifold, Review Research Fac. Sc., Yogoslavia, 15(1985), 203-178.
  • [7] M. Kobayashi, CR-submanifolds of a Sasakian manifold, Tensor N. S., 35(1981), 297-307.
  • [8] K. Matsumoto, On contact CR-submanifolds of Sasakian manifolds, Inter J. Math. § Math. Sci, 16(1983), 313-326.
  • [9] G. D. Ludden, Submanifolds of cosymplectic manifold, J. Diff. Geometry, 4(1970), 237-244.
  • [10] A. Cabras, A. Ianus and Gh. Pitis, Extrinsic spheres and parallel submanifolds in cosymplectic manifolds Math, J. Toyama Univ. 17(1994), 31-53.
  • [11] A. Bejancu and N. Papaghiuc, Semi-invariant submanifolds a Sasakian manifold, An. Sti. Univ. ’Al. I. Cuza’ Iasi Sect. Ia Mat. 27(1981), 163-170.
  • [12] A. Bejancu and N. Papaghiuc, Semi-invariant submanifolds a Sasakian space form, Colloq. Math. 48(1984), 77-88.
  • [13] N. Papaghiuc, Almost semi-invariant submanifolds in Sasakian Space forms, An. s¸t. Univ. Ias¸ı. 29(1983), 5-10.
  • [14] N. Papaghiuc, Some theorems on semi-invariant submanifolds of a Sasakian manifold, An. Sti. Univ. ’Al. I. Cuza’ Ias¸ı Sect. I a Mat. 32(1986), 73-76.
  • [15] C.L. Bejan,Almost semi-invariant submanifolds of a cosymplectic manifold, An. S¸ ti. Univ. ’Al. I. Cuza’ Iası Sect. I a Mat. 31(1985), 149-156.
  • [16] A. Cabras and P. Matzeu, Almost semi-invariant submanifolds of a cosymplectic manifold, Demonstratio Math. 19(1986), no.2, 395-401.
  • [17] B. B. Sinha and R.N. Yadav, Semi-invariant submanifolds of a Kenmotsu manifold, Bull. cal. Math. Soc. 86, 405-412, (1994).
  • [18] H. Öztürk, C. Murathan, N. Aktan, A.T. Vanli, Almost a-cosymplectic f -manifolds, Analele stııntıfıce ale unıversıtatıı ”AI.I Cuza” Dı ıas¸ı (S.N.) Matematica, Tomul LX, f.1. (2014).
  • [19] K. Yano, M. Kon, Structures on Manifolds, World Scientific, Singapore. (1984).
  • [20] K. I. Erken, P. Dacko and C. Murathan, Almost a-Paracosymplectic Manifolds, arXiv: 1402.6930v1.
  • [21] D.E. Blair, Geometry of Manifolds with structural group U(n)O(s), J.Differential Geometry, 4(1970), 155-167.
  • [22] A. Bejancu, Geometry of CR-Submanifolds, D.Reidel Publ. Co., Holland, 169p. (1986).

Semi-Invariant Submanifolds of Almost $\alpha$-Cosymplectic $f$-Manifolds

Year 2020, Volume: 3 Issue: 1, 57 - 66, 25.03.2020

Abstract

In this paper, we have and study several properties of semi-invariant submanifolds of an almost $\alpha$-cosymplectic $f$-manifold. We give an example and investigate the integrability conditions for the distributions involved in the definition of a semi-invariant submanifold of an almost $\alpha$-cosymplectic $f$-manifold.

References

  • [1] S. Lie, Geometrie der Beruhrungstransformationen. B.G. Teubner, Leipzig, (1896).
  • [2] H. Geiges, An Introduction to Contact Topology. Cambridge University Press, New York (2008).
  • [3] H. Geiges, A brief history of contact geometry and topology. Expo. Math. 19(1), 25-53 (2001).
  • [4] H. Geiges, Christiaan Huygens and contact geometry. Nieuw Arch. Wiskd (5). 6(2), 117-123. (2005).
  • [5] A. Bejancu, CR-submanifolds of a Kaehler manifold-I, Proc. Amer. Math. Soc., 69(1978), 135-42.
  • [6] M. H. Shahid, A. Sharfuddin and S.I. Husain, CR-submanifolds of a Sasakian manifold, Review Research Fac. Sc., Yogoslavia, 15(1985), 203-178.
  • [7] M. Kobayashi, CR-submanifolds of a Sasakian manifold, Tensor N. S., 35(1981), 297-307.
  • [8] K. Matsumoto, On contact CR-submanifolds of Sasakian manifolds, Inter J. Math. § Math. Sci, 16(1983), 313-326.
  • [9] G. D. Ludden, Submanifolds of cosymplectic manifold, J. Diff. Geometry, 4(1970), 237-244.
  • [10] A. Cabras, A. Ianus and Gh. Pitis, Extrinsic spheres and parallel submanifolds in cosymplectic manifolds Math, J. Toyama Univ. 17(1994), 31-53.
  • [11] A. Bejancu and N. Papaghiuc, Semi-invariant submanifolds a Sasakian manifold, An. Sti. Univ. ’Al. I. Cuza’ Iasi Sect. Ia Mat. 27(1981), 163-170.
  • [12] A. Bejancu and N. Papaghiuc, Semi-invariant submanifolds a Sasakian space form, Colloq. Math. 48(1984), 77-88.
  • [13] N. Papaghiuc, Almost semi-invariant submanifolds in Sasakian Space forms, An. s¸t. Univ. Ias¸ı. 29(1983), 5-10.
  • [14] N. Papaghiuc, Some theorems on semi-invariant submanifolds of a Sasakian manifold, An. Sti. Univ. ’Al. I. Cuza’ Ias¸ı Sect. I a Mat. 32(1986), 73-76.
  • [15] C.L. Bejan,Almost semi-invariant submanifolds of a cosymplectic manifold, An. S¸ ti. Univ. ’Al. I. Cuza’ Iası Sect. I a Mat. 31(1985), 149-156.
  • [16] A. Cabras and P. Matzeu, Almost semi-invariant submanifolds of a cosymplectic manifold, Demonstratio Math. 19(1986), no.2, 395-401.
  • [17] B. B. Sinha and R.N. Yadav, Semi-invariant submanifolds of a Kenmotsu manifold, Bull. cal. Math. Soc. 86, 405-412, (1994).
  • [18] H. Öztürk, C. Murathan, N. Aktan, A.T. Vanli, Almost a-cosymplectic f -manifolds, Analele stııntıfıce ale unıversıtatıı ”AI.I Cuza” Dı ıas¸ı (S.N.) Matematica, Tomul LX, f.1. (2014).
  • [19] K. Yano, M. Kon, Structures on Manifolds, World Scientific, Singapore. (1984).
  • [20] K. I. Erken, P. Dacko and C. Murathan, Almost a-Paracosymplectic Manifolds, arXiv: 1402.6930v1.
  • [21] D.E. Blair, Geometry of Manifolds with structural group U(n)O(s), J.Differential Geometry, 4(1970), 155-167.
  • [22] A. Bejancu, Geometry of CR-Submanifolds, D.Reidel Publ. Co., Holland, 169p. (1986).

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Selahattin BEYENDİ
inönü üniversitesi
0000-0002-1037-6410
Türkiye


Nesip AKTAN
Konya necmettin erbakan üniversitesi matematik bilgisayar bölümü
0000-0002-6825-4563
Türkiye


Ali İhsan SİVRİDAĞ This is me
İNÖNÜ ÜNİVERSİTESİ
Türkiye

Publication Date March 25, 2020
Submission Date February 17, 2020
Acceptance Date March 20, 2020
Published in Issue Year 2020 Volume: 3 Issue: 1

Cite

Bibtex @research article { cams690442, journal = {Communications in Advanced Mathematical Sciences}, issn = {2651-4001}, address = {}, publisher = {Emrah Evren KARA}, year = {2020}, volume = {3}, number = {1}, pages = {57 - 66}, title = {Semi-Invariant Submanifolds of Almost \$\\alpha\$-Cosymplectic \$f\$-Manifolds}, key = {cite}, author = {Beyendi, Selahattin and Aktan, Nesip and Sivridağ, Ali İhsan} }
APA Beyendi, S. , Aktan, N. & Sivridağ, A. İ. (2020). Semi-Invariant Submanifolds of Almost $\alpha$-Cosymplectic $f$-Manifolds . Communications in Advanced Mathematical Sciences , 3 (1) , 57-66 . Retrieved from https://dergipark.org.tr/en/pub/cams/issue/53344/690442
MLA Beyendi, S. , Aktan, N. , Sivridağ, A. İ. "Semi-Invariant Submanifolds of Almost $\alpha$-Cosymplectic $f$-Manifolds" . Communications in Advanced Mathematical Sciences 3 (2020 ): 57-66 <https://dergipark.org.tr/en/pub/cams/issue/53344/690442>
Chicago Beyendi, S. , Aktan, N. , Sivridağ, A. İ. "Semi-Invariant Submanifolds of Almost $\alpha$-Cosymplectic $f$-Manifolds". Communications in Advanced Mathematical Sciences 3 (2020 ): 57-66
RIS TY - JOUR T1 - Semi-Invariant Submanifolds of Almost $\alpha$-Cosymplectic $f$-Manifolds AU - SelahattinBeyendi, NesipAktan, Ali İhsanSivridağ Y1 - 2020 PY - 2020 N1 - DO - T2 - Communications in Advanced Mathematical Sciences JF - Journal JO - JOR SP - 57 EP - 66 VL - 3 IS - 1 SN - 2651-4001- M3 - UR - Y2 - 2020 ER -
EndNote %0 Communications in Advanced Mathematical Sciences Semi-Invariant Submanifolds of Almost $\alpha$-Cosymplectic $f$-Manifolds %A Selahattin Beyendi , Nesip Aktan , Ali İhsan Sivridağ %T Semi-Invariant Submanifolds of Almost $\alpha$-Cosymplectic $f$-Manifolds %D 2020 %J Communications in Advanced Mathematical Sciences %P 2651-4001- %V 3 %N 1 %R %U
ISNAD Beyendi, Selahattin , Aktan, Nesip , Sivridağ, Ali İhsan . "Semi-Invariant Submanifolds of Almost $\alpha$-Cosymplectic $f$-Manifolds". Communications in Advanced Mathematical Sciences 3 / 1 (March 2020): 57-66 .
AMA Beyendi S. , Aktan N. , Sivridağ A. İ. Semi-Invariant Submanifolds of Almost $\alpha$-Cosymplectic $f$-Manifolds. Communications in Advanced Mathematical Sciences. 2020; 3(1): 57-66.
Vancouver Beyendi S. , Aktan N. , Sivridağ A. İ. Semi-Invariant Submanifolds of Almost $\alpha$-Cosymplectic $f$-Manifolds. Communications in Advanced Mathematical Sciences. 2020; 3(1): 57-66.
IEEE S. Beyendi , N. Aktan and A. İ. Sivridağ , "Semi-Invariant Submanifolds of Almost $\alpha$-Cosymplectic $f$-Manifolds", Communications in Advanced Mathematical Sciences, vol. 3, no. 1, pp. 57-66, Mar. 2020
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