S. Deshmukh
Department of Mathematics, College of Science, King saud University, P.O. Box-2455, Riyadh-11451, Saudi Arabia.
[ 1 ] - On three-dimensional $N(k)$-paracontact metric manifolds and Ricci solitons
The aim of this paper is to characterize $3$-dimensional $N(k)$-paracontact metric manifolds satisfying certain curvature conditions. We prove that a $3$-dimensional $N(k)$-paracontact metric manifold $M$ admits a Ricci soliton whose potential vector field is the Reeb vector field $xi$ if and only if the manifold is a paraSasaki-Einstein manifold. Several consequences of this result are discuss...
[ 2 ] - Tangent Bundle of the Hypersurfaces in a Euclidean Space
Let $M$ be an orientable hypersurface in the Euclidean space $R^{2n}$ with induced metric $g$ and $TM$ be its tangent bundle. It is known that the tangent bundle $TM$ has induced metric $overline{g}$ as submanifold of the Euclidean space $R^{4n}$ which is not a natural metric in the sense that the submersion $pi :(TM,overline{g})rightarrow (M,g)$ is not the Riemannian submersion. In this paper...
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