Research Article

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

Volume: 3 Number: 1 March 25, 2020
Selahattin Beyendi *, Nesip Aktan , Ali İhsan Sivridağ
EN

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

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.

Keywords

Almost\ $\alpha$-cosypmlectic $f$-manifolds,Semi-invariant submanifolds,Integrability conditions

References

  1. [1] S. Lie, Geometrie der Beruhrungstransformationen. B.G. Teubner, Leipzig, (1896).
  2. [2] H. Geiges, An Introduction to Contact Topology. Cambridge University Press, New York (2008).
  3. [3] H. Geiges, A brief history of contact geometry and topology. Expo. Math. 19(1), 25-53 (2001).
  4. [4] H. Geiges, Christiaan Huygens and contact geometry. Nieuw Arch. Wiskd (5). 6(2), 117-123. (2005).
  5. [5] A. Bejancu, CR-submanifolds of a Kaehler manifold-I, Proc. Amer. Math. Soc., 69(1978), 135-42.
  6. [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. [7] M. Kobayashi, CR-submanifolds of a Sasakian manifold, Tensor N. S., 35(1981), 297-307.
  8. [8] K. Matsumoto, On contact CR-submanifolds of Sasakian manifolds, Inter J. Math. § Math. Sci, 16(1983), 313-326.
  9. [9] G. D. Ludden, Submanifolds of cosymplectic manifold, J. Diff. Geometry, 4(1970), 237-244.
  10. [10] A. Cabras, A. Ianus and Gh. Pitis, Extrinsic spheres and parallel submanifolds in cosymplectic manifolds Math, J. Toyama Univ. 17(1994), 31-53.
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. https://izlik.org/JA58KZ59KK
AMA
1.Beyendi S, Aktan N, Sivridağ Aİ. Semi-Invariant Submanifolds of Almost $\alpha$-Cosymplectic $f$-Manifolds. Communications in Advanced Mathematical Sciences. 2020;3(1):57-66. https://izlik.org/JA58KZ59KK
Chicago
Beyendi, Selahattin, Nesip Aktan, and Ali İhsan Sivridağ. 2020. “Semi-Invariant Submanifolds of Almost $\alpha$-Cosymplectic $f$-Manifolds”. Communications in Advanced Mathematical Sciences 3 (1): 57-66. https://izlik.org/JA58KZ59KK.
EndNote
Beyendi S, Aktan N, Sivridağ Aİ (March 1, 2020) Semi-Invariant Submanifolds of Almost $\alpha$-Cosymplectic $f$-Manifolds. Communications in Advanced Mathematical Sciences 3 1 57–66.
IEEE
[1]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, [Online]. Available: https://izlik.org/JA58KZ59KK
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 1, 2020): 57-66. https://izlik.org/JA58KZ59KK.
JAMA
1.Beyendi S, Aktan N, Sivridağ Aİ. Semi-Invariant Submanifolds of Almost $\alpha$-Cosymplectic $f$-Manifolds. Communications in Advanced Mathematical Sciences. 2020;3:57–66.
MLA
Beyendi, Selahattin, et al. “Semi-Invariant Submanifolds of Almost $\alpha$-Cosymplectic $f$-Manifolds”. Communications in Advanced Mathematical Sciences, vol. 3, no. 1, Mar. 2020, pp. 57-66, https://izlik.org/JA58KZ59KK.
Vancouver
1.Selahattin Beyendi, Nesip Aktan, Ali İhsan Sivridağ. Semi-Invariant Submanifolds of Almost $\alpha$-Cosymplectic $f$-Manifolds. Communications in Advanced Mathematical Sciences [Internet]. 2020 Mar. 1;3(1):57-66. Available from: https://izlik.org/JA58KZ59KK