Real Hypersurfaces of Complex Space Forms in Terms of Ricci $*$-Tensor
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Cites background from "Real Hypersurfaces of Complex Space..."
...Hamada [11] on real hypersurfaces of non-flat complex space forms....
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Cites background from "Real Hypersurfaces of Complex Space..."
...is the dimension of manifold. The notion of ∗-Ricci tensor on almost Hermitian manifolds and ∗-Ricci tensor of real hypersurfaces in non-flat complex space were introduced by Tachibana [14] and Hamada [5] respectively where the ∗-Ricci tensor is defined by: S∗(X,Y) = 1 2 (trace{φ◦R(X,φY)}), (1.7) for all vector fields X,Y on Mn and φ is a (1,1)-tensor field. If S∗(X,Y) = λg(X,Y) + µη(X)η(Y) for all vecto...
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"Real Hypersurfaces of Complex Space..." refers background in this paper
... persurfaces in Pn(C), The proof can be found in [ 2 ]....
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...that there are no Einstein real hypersurfaces of Pn(C) [ 2 ]....
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"Real Hypersurfaces of Complex Space..." refers background in this paper
...Proposition 2.9. ([ 3 ]) Let M be a real hypersurface of Pn(C)....
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"Real Hypersurfaces of Complex Space..." refers background in this paper
...Proposition 2.3. ([ 6 ], [9]) Let M, where n ‚ 2, be a real hypersurface in Mn(c) of constant holomorphic sectional curvature 4c 6= 0. Then `A = A` if and only if M is an open subset of the following: (i) a geodesic hypersphere, (ii) a tube over totally geodesic complex space form Mk(c), where 0 < k • ni1....
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"Real Hypersurfaces of Complex Space..." refers background in this paper
...Proposition 2.10. ([ 1 ]) Let M be a real hypersurface of Hn(C) of constant holomorphic sectional curvature 4c < 0. Then M has constant principal curvatures and » is a principal curvature vector if and only if M is locally congruent to the following:...
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