Results on Invariant Submanifolds of Hyperbolic Kenmotsu Manifolds

Authors

DOI:

https://doi.org/10.26713/cma.v15i4.3280

Keywords:

Hyperbolic Kenmotsu manifold, Invariant submanifold, Totally geodesic submanifold

Abstract

In this paper, our main focus was on studying the geodesic property of invariant submanifolds of Hyperbolic Kenmotsu manifolds. We also investigated different conditions regarding the second fundamental form \(\pi\) and established its equivalence. These conditions included being 2-semiparallel, pseudoparallel, 2-pseudoparallel, Ricci-generalized pseudoparallel and 2-Ricci-generalized pseudoparallel.

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References

C. Özgür and C. Murathan, On invariant submanifolds of Lorentzian Para-Sasakian manifolds, The Arabian Journal for Science and Engineering 34(2A) (2009), 177 – 185.

K. Arslan, Ü. Lumiste, C. Murathan and C. Özgür, 2-Semiparallel Surfaces in Space Forms: 1. Two particular pages, Proceedings of the Estonian Academy of Sciences. Physics. Mathematics 49(3) (2000), 139 – 148, DOI: 10.3176/phys.math.2000.3.01.

A. C. Asperti, G. A. Lobos and F. Mercuri, Pseudo-Parallel Submanifolds of a Space Form, Advances in Geometry 2(1) (2001), 57 – 71, DOI: 10.1515/ADVG.2001.027.

L. Bhatt and K. K. Dube, On CR-submanifolds of a trans hyperbolic Sasakian manifold, Acta Ciencia Indica Mathematics 29(1) (2003), 91 – 96.

S. K. Chaubey, D. M. Siddiqi and D. G. Prakasha, Invariant submanifolds of hyperbolic Sasakian manifolds and η-Ricci-Bourguignon solitons, Filomat 36(2) (2022), 409 – 421, DOI: 10.2298/FIL2202409C.

B.-Y. Chen, A simple characterization of generalized Robertson–Walker spacetimes, General Relativity and Gravitation 46 (2014), article number 1833, DOI: 10.1007/s10714-014-1833-9.

J. Deprez, Semi-parallel surfaces in the Euclidean space, Journal of Geometry 25 (1985), 192 – 200, DOI: 10.1007/BF01220480.

H. Gill and K. K. Dube, Generalized CR-submanifolds of the trans hyperbolic Sasakian manifold, Demonstratio Mathematica 38(4) (2005), 953 – 960, DOI: 10.1515/dema-2005-0420.

C. Murathan, A. Arslan and R. Ezentas, Ricci generalized pseudo-parallel immersions, in: Proceedings of the 9th International Conference on Differential Geometry and Its Applications, Prague, Matfyzpress, pp. 99 – 108 (2005).

Pankaj, S. K. Chaubey and G. Ayar, Yamabe and gradient Yamabe solitons on 3-dimensional hyperbolic Kenmotsu manifolds, Differential Geometry – Dynamical Systems 23 (2021), 176 – 184.

W. Roter, On conformally recurrent Ricci-recurrent manifolds, Colloquium Mathematicum 46 (1982), 45 – 57, DOI: 10.4064/CM-46-1-45-57.

M. D. Siddiqi and M. A. Akyol, Anti-invariant ξ⊥-Riemannian submersions from hyperbolic β-Kenmotsu manifolds, Cubo (Temuco) 20(1) (2018), 79 – 94, DOI: 10.4067/S0719-06462018000100079.

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Published

15-12-2024
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How to Cite

Aishwarya, C., & Venkatesha, V. (2024). Results on Invariant Submanifolds of Hyperbolic Kenmotsu Manifolds. Communications in Mathematics and Applications, 15(4), 1373–1381. https://doi.org/10.26713/cma.v15i4.3280

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Research Article