Real Hypersurfaces of Complex Space Forms in Terms of Ricci $*$-Tensor
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Cites background from "Real Hypersurfaces of Complex Space..."
...Later, in [17] Hamada studied ∗-Ricci flat real hypersurfaces in non-flat complex space forms and Blair [4] defined ∗-Ricci tensor in contact metric manifolds by S∗(X,Y ) = g(Q∗X,Y ) = Trace{φ ◦R(X,φY )}, (1....
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Cites background from "Real Hypersurfaces of Complex Space..."
..., the ∗-Ricci tensor satisfies S∗ = ρ∗g, with ρ∗ being constant, are introduced and the real hypersurfaces are studied with respect to the previous relations (see [10,11,15])....
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...In [10] Hamada gave the definition of ∗-Ricci tensor S∗ on real hypersurfaces in Mn(c) in the following way g(S∗X, Y) = 1 2 trace(Z → R(X, φY)φZ),...
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References
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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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284 citations
"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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282 citations
"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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253 citations
"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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