Real hypersurfaces in a nonflat complex space form and their almost contact metric structures

2011 ◽  
Vol 124 (1) ◽  
pp. 117-131
Author(s):  
Young Ho Kim ◽  
Sadahiro Maeda
Keyword(s):  
Complex Space ◽  
Space Form ◽  
Complex Space Form ◽  
Real Hypersurfaces ◽  
Almost Contact Metric ◽  
Metric Structures ◽  
Almost Contact Metric Structures

scholarly journals Real hypersurfaces of indefinite Kaehler manifolds

1993 ◽  
Vol 16 (3) ◽  
pp. 545-556 ◽  
Author(s):  
A. Bejancu ◽  
K. L. Duggal
Keyword(s):  
Complex Space ◽  
Parallel Structure ◽  
Real Hypersurfaces ◽  
Sasakian Manifolds ◽  
Space Forms ◽  
Kaehler Manifolds ◽  
Almost Contact Metric ◽  
Metric Structures ◽  
Complex Space Forms ◽  
Almost Contact Metric Structures

We show the existence of ( ϵ )-almost contact metric structures and give examples of ( ϵ )-Sasakian manifolds. Then we get a classification theorem for real hypersurfaces of indefinite complex space-forms with parallel structure vector field. We prove that ( ϵ )-Sasakian real hypersurfaces of a semi-Euclidean space are either open sets of the pseudosphereS2S2n+1(1) or of the pseudohyperbolic spaceH2S−12n+1(1). Finally, we get the causal character of ( ϵ ) cosymplectic real hypersurfaccs of indefinite complex space-forms.

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

1994 ◽  
Vol 37 (2) ◽  
pp. 238-244 ◽  
Author(s):  
U-Hang Ki ◽  
Young-Jin Suh
Keyword(s):  
Complex Space ◽  
Space Form ◽  
Type A ◽  
Complex Space Form ◽  
Real Hypersurfaces ◽  
Orthogonal Distribution

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.

Remarks on η-parallel real hypersurfaces in ℂP2 and ℂH2

2020 ◽  
Vol 17 (05) ◽  
pp. 2050073
Author(s):  
Yaning Wang
Keyword(s):  
Complex Space ◽  
Space Form ◽  
Three Dimensional ◽  
Shape Operator ◽  
Complex Space Form ◽  
Real Hypersurfaces ◽  
Geodesic Sphere ◽  
Principal Curvatures ◽  
Space Forms ◽  
Complex Dimension

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].

scholarly journals Ricci operator in a Hopf real Hypersurfaces of complex space form

2020 ◽  
Vol 1597 ◽  
pp. 012049
Author(s):  
Uppara Manjulamma ◽  
H G Nagaraja ◽  
D L Kiran Kumar
Keyword(s):  
Complex Space ◽  
Space Form ◽  
Complex Space Form ◽  
Real Hypersurfaces ◽  
Ricci Operator
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