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On some Lr-biharmonic Euclidean hypersurfaces

Mohammadpouri A., Pashaie F.

Journal of Mathematics and Applications

2016

Vol. 39

91--104

In decade eighty, Bang-Yen Chen introduced the concept of biharmonic hypersurface in the Euclidean space. An isometrically immersed hypersurface x : Mn → En+1 is said to be biharmonic if ∆2x = 0, where ∆ is the Laplace operator. We study the Lr-biharmonic hypersurfaces as a generalization of biharmonic ones, where Lr is the linearized operator of the (r + 1)th mean curvature of the hypersurface and in special case we have L0 = ∆. We prove that Lr-biharmonic hypersurface of Lr-finite type and also Lr-biharmonic hypersurface with at most two distinct principal curvatures in Euclidean spaces are r-minimal.

Submanifolds immersed in a generalized Hsu quaternion manifold

Das L., Nivas R., Mishra M.

Demonstratio Mathematica

2006

Vol. 39, nr 3

639-642

Integrability conditions of an almost quarternion manifold were studied by Yano and Ako [7]. Hamoui [1] and others have studied quaternion submanifolds of codimension 2 [1]. Vanzura [5] defined and have studied almost r- contact structure on manifolds. In this paper we have defined the Hsu-quaternion manifold and studied the submanifolds of codimension p immersed in a generalized Hsu quaternion manifold. Certain other interesting results have also been established.

Semi-slant submanifolds of t-manifolds

Khan V., Khan M.

Demonstratio Mathematica

2006

Vol. 39, nr 4

907-918

J. L. Cabrerizo et al. [5] studied slant submanifolds of Sasakian and K- contact manifolds. Semi-slant submanifolds were introduced as a generalized version of CR-submanifold. Cabrerizo et al. [4] obtained interesting results for the semi-slant submanifold of Sasakian manifolds. The purpose of the present paper is to study slant and semi-slant submanifolds of a T-manifold.

Generalized CR-submanifolds of the trans hyperbolic Sasakian manifold

Gill H., Dube K.

Demonstratio Mathematica

2005

Vol. 38, nr 4

953--960

The purpose of the present paper is to study generalized CR- submanifolds of the trans hyperbolic Sasakian manifold and obtained their basic properties. The conditions under which the distribution of generalized CR-submanifolds of the trans hyperbolic Sasakian manifold is integrable have been obtained. Totally geodesic generalized CR- submanifolds of the trans hyperbolic Sasakian manifold have also been studied.