Sharief Deshmukh

Bio: Sharief Deshmukh is an academic researcher from King Saud University. The author has contributed to research in topics: Ricci curvature & Scalar curvature. The author has an hindex of 15, co-authored 119 publications receiving 820 citations. Previous affiliations of Sharief Deshmukh include West University of Timișoara.

Yamabe and Quasi-Yamabe Solitons on Euclidean Submanifolds

Abstract: In this paper, we initiate the study of Yamabe and quasi-Yamabe solitons on Euclidean submanifolds whose soliton fields are the tangential components of their position vector fields. Several fundamental results of such solitons were proved. In particular, we classify such Yamabe and quasi-Yamabe solitons on Euclidean hypersurfaces.

On rectifying curves in Euclidean 3-space

Abstract: First, we study rectifying curves via the dilation of unit speed curves on the unit sphere S in the Euclidean space E . Then we obtain a necessary and sufficient condition for which the centrode d(s) of a unit speed curve α(s) in E is a rectifying curve to improve a main result of [4]. Finally, we prove that if a unit speed curve α(s) in E is neither a planar curve nor a helix, then its dilated centrode β(s) = ρ(s)d(s) , with dilation factor ρ , is always a rectifying curve, where ρ is the radius of curvature of α .

Reduction in codimension of mixed foliate CR-submanifolds of a Kaehler manifold

Abstract: Starting with a proper mixed foliate Ci?-submanifold M of dimension 2p-\-q in a hyperbolic complex space form M(—4) of dimension m(rn^2p+2q), it has been proved that under a suitable condition on second fundamental form there exists a (2p+2q) -dimensional totally geodesic submanifold M' of M such that Mis a mixed foliate Ctf-submanifold of M'.

Ricci solitons and concurrent vector fields

Abstract: A Ricci soliton $(M^n,g,v,\lambda)$ on a Riemannian manifold $(M^n,g)$ is said to have concurrent potential field if its potential field $v$ is a concurrent vector field. In the first part of this paper we completely classify Ricci solitons with concurrent potential fields. In the second part we derive a necessary and sufficient condition for a submanifold to be a Ricci soliton in a Riemannian manifold equipped with a concurrent vector field. In the last part, we classify shrinking Ricci solitons with $\lambda=1$ on Euclidean hypersurfaces. Several applications of our results are also presented.

The Foundations Of Differential Geometry

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Real Hypersurfaces in Complex Space Forms

Abstract: The study of real hypersurfaces in complex projective space CP n and complex hyperbolic space CH n began at approximately the same time as Munzner’s work on isoparametric hypersurfaces in spheres. A key early work was Takagi’s classification [669] in 1973 of homogeneous real hypersurfaces in CP n . These hypersurfaces necessarily have constant principal curvatures, and they serve as model spaces for many subsequent classification theorems. Later Montiel [501] provided a similar list of standard examples in complex hyperbolic space CH n . In this chapter, we describe these examples of Takagi and Montiel in detail, and later we prove many important classification results involving them. We also study Hopf hypersurfaces, focal sets, parallel hypersurfaces and tubes using both standard techniques of submanifold geometry and the method of Jacobi fields.