• Mukut Mani Tripathi

      Articles written in Proceedings – Mathematical Sciences

    • A basic inequality for submanifolds in locally conformal almost cosymplectic manifolds

      Mukut Mani Tripathi Jeong-Sik Kim Seon-Bu Kim

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      For submanifolds tangent to the structure vector field in locally conformal almost cosymplectic manifolds of pointwise constantφ-sectional curvature, we establish a basic inequality between the main intrinsic invariants of the submanifold on one side, namely its sectional curvature and its scalar curvature; and its main extrinsic invariant on the other side, namely its squared mean curvature. Some applications including inequalities between the intrinsic invariantδM and the squared mean curvature are given. The equality cases are also discussed.

    • The Structure of some Classes of 𝐾-Contact Manifolds

      Mukut Mani Tripathi Mohit Kumar Dwivedi

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      We study projective curvature tensor in 𝐾-contact and Sasakian manifolds. We prove that (1) if a 𝐾-contact manifold is quasi projectively flat then it is Einstein and (2) a 𝐾-contact manifold is 𝜉-projectively flat if and only if it is Einstein Sasakian. Necessary and sufficient conditions for a 𝐾-contact manifold to be quasi projectively flat and 𝜑-projectively flat are obtained. We also prove that for a $(2n+1)$-dimensional Sasakian manifold the conditions of being quasi projectively flat, 𝜑-projectively flat and locally isometric to the unit sphere $S^{2n+1}(1)$ are equivalent. Finally, we prove that a compact 𝜑-projectively flat 𝐾-contact manifold with regular contact vector field is a principal $S^1$-bundle over an almost Kaehler space of constant holomorphic sectional curvature 4.

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