Let M be a complete hypersurface with constant normalized scalar curvature R in a hyperbolic space form H. We prove that if R̄ = R + 1 ≥ 0 and the norm square |h| of the second fundamental form of M satisfies nR̄ ≤ sup |h| ≤ n (n− 2)(nR̄− 2) [n(n− 1)R̄ − 4(n− 1)R̄ + n], then either sup |h| = nR̄ and M is a totally umbilical hypersurface; or sup |h| = n (n− 2)(nR̄− 2) [n(n− 1)R̄ − 4(n− 1)R̄ + n], and M i...

In this paper, we study geodesic contact CR-lightlike submanifolds and geodesic screen CR-lightlike (SCR) submanifolds of indefinite Sasakian manifolds. Some necessary and sufficient conditions for totally geodesic, mixed geodesic, D -geodesic and -geodesic contact CR-lightlike submanifolds and SCR submanifolds are obtained. D

The Riemannian product $${\mathbb{M}}_1(c_1) \times {\mathbb{M}}_2(c_2)$$ , where $${\mathbb{M}}_i(c_i)$$ denotes the 2-dimensional space form of constant sectional curvature $$c_i \in {\mathbb{R}}$$ has two different $${\mathrm{Spin}^{\mathrm{c}}}$$ structures carrying each a parallel spinor. restriction these spinor fields to 3-dimensional hypersurface M characterizes isometric immersion into...

We study screen homothetic half lightlike submanifolds of indefinite Kenmotsu manifolds. Two natural conditions to impose on this study are that its homothetic factor be either non-zero constant or zero, the latter is equivalent to the screen distribution to be totally geodesic. The purpose of this paper is to prove that there do not exist above two types screen homothetic half lightlike subman...

A k-harmonic map is a critical point of the k-energy defined on space smooth maps between two Riemannian manifolds. In this paper, we prove that if $$M^{n} (n\ge 3)$$ CMC proper triharmonic hypersurface with at most three distinct principal curvatures in form $$\mathbb {R}^{n+1}(c)$$ , then M has constant scalar curvature. This supports generalized Chen’s conjecture when $$c\le 0$$ . When $$c=1...

In this paper we introduce the notion of screen pseudo-slant lightlike submanifolds of indefinite Kaehler manifolds giving characterization theorem with some non-trivial examples of such submanifolds. Integrability conditions of distributions D1, D2 and RadTM on screen pseudo-slant lightlike submanifolds of an indefinite Kaehler manifold have been obtained. Further, we obtain necessary and suff...

Abstract Lightlike hypersurfaces in semi-Riemannian manifolds admitting concircular vector fields are investigated. We prove that such generally products of lightlike curves and warped product manifolds. In special cases, we show these totally geodesic or screen provided belong to their normal transversal bundles. A number examples furnished, where possible, illustrate the main concepts.

In this paper we extend the study of the indicatrix of a complex Finsler space initiated in [10, 11]. The equations that can be introduced on the indicatrix, which is studied as a hypersurface of a complex Finsler space, are investigated. In this manner, using the equations of Gauss-Weingarten, the link between the intrinsic and induced connection is deduced. The equations of Gauss, H -and A-Co...