Four constructions of constant mean curvature (CMC) hypersurfaces in S are given, which should be considered analogues of ‘classical’ constructions that are possible for CMC hypersurfaces in Euclidean space. First, Delaunay-like hypersurfaces, consisting roughly of a chain of hyperspheres winding multiple times around an equator, are shown to exist for all values of the mean curvature. Second, ...

This is a survey on harmonic maps and biharmonic maps into (1) Riemannian manifolds of non-positive curvature, (2) compact Lie groups or (3) compact symmetric spaces, based mainly on my recent works on these topics.

Four constructions of constant mean curvature (CMC) hypersurfaces in Sn+1 are given, which should be considered analogues of ‘classical’ constructions that are possible for CMC hypersurfaces in Euclidean space. First, Delaunay-like hypersurfaces, consisting roughly of a chain of hyperspheres winding multiple times around an equator, are shown to exist for all the values of the mean curvature. S...

In this paper, we introduce semi-symmetric metric Koszul forms and non-metric on singular semi-Riemannian manifolds. Semi-symmetric their curvature of semi-regular warped products are expressed in terms those the factor We also associated to almost product structure Furthermore, generalize results \cite{St2} multiply products.

We construct series of examples of exotic smooth structures on compact locally symmetric spaces of noncompact type. In particular, we obtain higher rank examples, which do not support Riemannian metric of nonpositive curvature. The examples are obtained by taking the connected sum with an exotic sphere. To detect the change of the smooth structure we use a tangential map from the locally symmet...

In this article, we derive Chen’s inequalities involving ?-invariant ?M, Riemannian invariant ?(m1,?,mk), Ricci curvature, ?k(2?k?m), the scalar curvature and squared of mean for submanifolds generalized Sasakian-space-forms endowed with a quarter-symmetric connection. As an application obtain inequality, first derived Chen inequality bi-slant submanifold Sasakian-space-forms.

The Lemaître-Tolman-Bondi (LTB) model represents an inhomogeneous spherically symmetric universefilledwithfreelyfallingdustlikematterwithoutpressure. First,wehaveconsideredaFinslerian anstaz of (LTB) and have found a Finslerian exact solution of vacuum field equation. We have obtained the R(t,r) and S(t,r) with considering establish a new solution of Rµν = 0. Moreover, we attempttouseFinslergeo...

The aim of this paper is to construct two functors, called the derived functors of anchored modules which allow linear connections. Some applications are given in the cases of vector bundles with differentials and Lie algebras. It is also shown that a linear connection and a skew-symmetric form on a preinfinitesimal module lift on the derived Lie pseudoalgebra to a null curvature connection and...

We show that under suitable conditions a branched cover satisses the same upper curvature bounds as its base space. First we do this when the base space is a metric space satisfying Alexandrov's curvature condition CAT() and the branch locus is complete and convex. Then we treat branched covers of a Riemannian manifold over suitable mutually orthogonal submanifolds. In neither setting do we req...

In this paper, first we give a notion for linear Weingarten spacelike hypersurfaces with P + aH = b in a locally symmetric Lorentz space Ln+1 1 . Furthermore, we study complete or compact linear Weingarten spacelike hypersurfaces in locally symmetric Lorentz spaces Ln+1 1 satisfying some curvature conditions. By modifying Cheng-Yau’s operator given in [7], we introduce a modified operator L and...