Certain Results for Invariant Submanifolds of an Almost $\alpha$-Cosymplectic $(k,\mu ,\nu )$-Space

Year 2024, Volume: 12 Issue: 2, 93 - 100, 14.04.2024

Pakize Uygun , Mehmet Atçeken , Tuğba Mert

https://doi.org/10.36753/mathenot.1395051

Abstract

In this paper we present invariant submanifolds of an almost $\alpha $-cosymplectic $(k, \mu, \nu)$-space. Then, we gave some results for an invariant submanifold of an almost $\alpha $-cosymplectic $(k,\mu,\nu)$-space to be totally geodesic. As a result, we have discovered some interesting conclusions about invariant submanifolds of an almost cosymplectic $(k, \mu, \nu)$-space.

Keywords

$W_{1}^{\ast }$-curvature tensor, $\alpha$-cosymlectic $(k,\mu,\nu)$-space, $W_{7}$-curvature tensor

References

• [1] Koufogiorgos, T., Tsichlias, C.: On the existence of a new class of contact metric manifolds. Canadian Mathematical Bulletin. 43(4), 440-447 (2000).
• [2] Goldberg, S.I., Yano, K.: Integrability of almost cosymplectic strustures. Pacific Journal of Mathematics. 31, 373-382 (1969).
• [3] Küpeli Erken, I.: On a classıfıcation of almost $\alpha -$ cosymplectic manifolds. Khayyam Journal of Mathematics. 5(1), 1-10 (2019).
• [4] Olszak, Z.: On almost cosymplectic manifolds. Kodai Mathematical Journal. 4, 239-250 (1981).
• [5] Atçeken, M.: Characterizations for an invariant submanifold of an almost $\alpha -$cosymplectic $(k,\mu ,\nu )-$ space to be totally geodesic. Filomat. 36(9), 2871-2879 (2022).
• [6] Aktan, N., Balkan, S., Yildirim, M.: On weakly symmetries of almost Kenmotsu $(k,\mu ,\nu )-$spaces. Hacettepe Journal of Mathematics and Statistics. 42(4), 447-453 (2013).
• [7] Atçeken, M.: Certain results on invariant submanifolds of an almost Kenmotsu $(k,\mu ,\nu )-$space. Arabian Journal of Mathematics. 10, 543-554 (2021).
• [8] Yıldırım, M., Aktan, N.: Holomorphically planar conformal vector field on almost $\alpha $-cosymplectic $(k,\mu ,\nu )-$spaces. Fundamental Journal of Mathematics and Applications. 6(1), 35-41 (2023).
• [9] Carriazo, A., Martin-Molina, V.: Almost cosymplectic and almost Kenmotsu $(k,\mu ,\nu )-$space. Mediterranean Journal of Mathematics. 10, 1551-1571 (2013).
• [10] Dacko, P., Olszak, Z.: On almost cosymplectic $(k,\mu ,\nu )-$spaces. Banach Center Publications. 69(1), 211-220 (2005).
• [11] Kim, T.W., Pak, H.K: Canonical foliations of certain classses of almost contact metric structures. Acta Mathematica Sinica, English Series. 21(4), 841-856 (2005).
• [12] Öztürk, H., Aktan, N., Murathan, C.: Almost $\alpha -$% cosymplectic $(k,\mu ,\nu )-$spaces. ArXiv: 10077. 0527 v1.
• [13] Koufogiorgos, T., Markellos, M., Papantoniou, V.J.: The harmonicity of the Reeb vector fields on contact 3- manifolds. Pacific Journal of Mathematics. 234(2), 325-344 (2008).
• [14] Pokhariyal, G.P., Mishra, R.S.: Curvature tensors and their relativistic significance II. Yokohama Mathematical Journal. 19(2), 97-103 (1971).
• [15] Pokhariyal, G.P.: Relativistic significance of curvature tensors. International Journal of Mathematics and Mathematical Sciences. 5(1), 133-139 (1982).