1 results
Generalized
${\mathcal{D}}$-Einstein Real Hypersurfaces in 
$\mathbb{C}P^{2}$ and 
$\mathbb{C}H^{2}$
- Part of
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- Journal:
- Canadian Mathematical Bulletin / Volume 63 / Issue 4 / December 2020
- Published online by Cambridge University Press:
- 27 February 2020, pp. 909-920
- Print publication:
- December 2020
-
- Article
- Export citation
-
In this paper we obtain some new characterizations of pseudo-Einstein real hypersurfaces in
$\mathbb{C}P^{2}$ and 
$\mathbb{C}H^{2}$. More precisely, we prove that a real hypersurface in 
$\mathbb{C}P^{2}$ or 
$\mathbb{C}H^{2}$ with constant mean curvature is generalized 
${\mathcal{D}}$-Einstein with constant coefficient if and only if it is pseudo-Einstein. We prove that a real hypersurface in 
$\mathbb{C}P^{2}$ with constant scalar curvature is generalized 
${\mathcal{D}}$-Einstein with constant coefficient if and only if it is pseudo-Einstein.
