# Real Hypersurfaces of Complex Space Forms in Terms of Ricci $*$-Tensor

TL;DR: In this article, the authors classified the $*$-Einstein real hypersurfaces in complex space forms such that the structure vector is a principal curvature vector and the principal curvatures of the hypersurface can be computed with the K\"ahler metric.

Abstract: It is known that there are no Einstein real hypersurfaces in complex space forms equipped with the K\"ahler metric. In the present paper we classified the $*$-Einstein real hypersurfaces $M$ in complex space forms $M_{n}(c)$ and such that the structure vector is a principal curvature vector.

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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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