Characterization Of Real Hypersurfaces Research Articles

New characterizations of real hypersurfaces with isometric Reeb flow in the complex quadric

We prove an integral inequality for compact orientable real hypersurfaces of the complex quadric $Q^n\ (n\ge 3)$ in terms of their shape operator $S$ and Reeb vector field $\xi $. As direct consequences, we obtain new characterizations for real

Remarks on η-parallel real hypersurfaces in ℂP2 and ℂH2

Let [Formula: see text] be a three-dimensional real hypersurface in a nonflat complex space form of complex dimension two. In this paper, we prove that [Formula: see text] is [Formula: see text]-parallel with two distinct principal curvatures at each point if and only if it is locally congruent to a geodesic sphere in [Formula: see text] or a horosphere, a geodesic sphere or a tube over totally geodesic complex hyperbolic plane in [Formula: see text]. Moreover, [Formula: see text]-parallel real hypersurfaces in [Formula: see text] and [Formula: see text] under some other conditions are classified and these results extend Suh’s in [Characterizations of real hypersurfaces in complex space forms in terms of Weingarten map, Nihonkai Math. J. 6 (1995) 63–79] and Kon–Loo’s in [On characterizations of real hypersurfaces in a complex space form with [Formula: see text]-parallel shape operator, Canad. Math. Bull. 55 (2012) 114–126].

Certain types of real hypersurfaces in complex space forms

A nice characterization of real hypersurfaces of a nonflat complex space form is very much familiar when its structure vector field $$\xi $$ is Killing. This motivates us to classify a real hypersurface of a nonflat complex space form when the structure vector field $$\xi $$ is 2-Killing (i.e., $$\pounds _{\xi }\pounds _{\xi }g = 0)$$ , where $$\pounds _{\xi }$$ denotes the Lie derivative along the vector field $$\xi $$ . Further, we classify real hypersurfaces of a nonflat complex space form when the tensor field $$T (= \pounds _{\xi }g)$$ is (i) weakly Lie $$\xi $$ -parallel, and (ii) weakly parallel.

Characterizations of real hypersurfaces with the composition of structure Lie operator in nonflat complex space form

Characterizations of real hypersurfaces with the composition of structure Lie operator in nonflat complex space form

Characterization of real hypersurface with anti-derivatives of structure Lie operator in a complex space form

Characterization of real hypersurface with anti-derivatives of structure Lie operator in a complex space form

Characterizations of Real Hypersurfaces in a Complex Space Form

AbstractWe study a real hypersurface M in a complex space form Mn(c), c ≠ 0, whose shape operator and structure tensor commute each other on the holomorphic distribution of M.

On real hypersurfaces in a quaternionic hyperbolic space in terms of the derivative of the second fundamental tensor

The purpose of this paper is to give a characterization of real hypersurfaces of type A0, A in a quaternionic hyperbolic spaceQHm by the covariant derivative of the second fundamental tensor.

Some Conditions on Real Hypersurfaces in Quaternionic Projective Spaces in Terms of Lie Derivatives

The purpose of this paper is to give a non-existence property with the Lie derivative of the structure tensors φi and some characterizations of real hypersurfaces of type A1, A2 in a quaternionic projective space QPm in terms of the Lie derivatives of the second fundamental tensor A and the induced Riemannian metric g on the distribution D⊥ = Span {U2, U2, U3}.

A Characterization of Real Hypersurfaces in Complex Space Forms in Terms of the Ricci Tensor

AbstractWe study real hypersurfaces of a complex space form Mn(c), c ≠ 0 under certain conditions of the Ricci tensor on the orthogonal distribution T0.

Characterizations of real hypersurfaces in complex space forms in terms of curvature tensors

Characterizations of real hypersurfaces in complex space forms in terms of curvature tensors

On a Characterization of Real Hypersurfaces of Type a in a Complex Space Form

AbstractIn this paper, under certain conditions on the orthogonal distribution T0, we give a characterization of real hypersurfaces of type A in a complex space form Mn(c), c ≠ 0.