Curvature Invariance of Invariant Hypersurfaces in 3-Dimensional LP-Sasakian Space Forms

Authors

  • S. N. Manjunath   Lecturer, Department of Science, Govt. VISSJ Polytechnic, Bhadravathi, Karnataka, India.

Keywords:

Invariant, hypersurface, L P-Sasakian manifold.

Abstract

In this work, we investigate the geometric properties of invariant hypersurfaces within 3-dimensional Lorentzian para-Sasakian (LP-Sasakian) space forms. Specifically, we establish that if M ̅ is an invariant hypersurface of a 3-dimensional LP-Sasakian manifold M with constant φ-sectional curvature, then M ̅is curvature-invariant. Utilizing the Gauss equation and the structural compatibility of the LP-Sasakian manifold, it is shown that the curvature tensor of M ̅retains the essential features of the ambient curvature tensor of M, ensuring that M ̅ preserves the curvature characteristics of the ambient space. This result highlights the geometric rigidity and intrinsic curvature symmetry of invariant hypersurfaces in LP-Sasakian geometry.

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International Journal of Scientific Research in Science and Technology

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Published

2021-07-30

Issue

Volume 8, Issue 4, July-August-2021

Section

Research Articles

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How to Cite

[1]
S. N. Manjunath "Curvature Invariance of Invariant Hypersurfaces in 3-Dimensional LP-Sasakian Space Forms" International Journal of Scientific Research in Science and Technology(IJSRST), Online ISSN : 2395-602X, Print ISSN : 2395-6011,Volume 8, Issue 4, pp.781-786, July-August-2021.