Paper · Oct 29, 2017

Real hypersurfaces of complex quadric in terms of star-Ricci tensor

Xiaomin Chen

math.DGarXiv:1710.10627
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Abstract

In this article, we introduce the notion of star-Ricci tensors in the real hypersurfaces of complex quadric . It is proved that there exist no Hopf hypersurfaces in , with commuting star-Ricci tensor or parallel star-Ricci tensor. As a generalization of star-Einstein metric, star-Ricci solitons on are considered. In this case we show that is an open part of a tube around a totally geodesic .

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Submitted
Oct 29, 2017
Subjects
math.DG

Comments: 13 pages, accepted by Tokyo Journal of Mathematics

Ricci solitonsEinstein metrics

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Read around it

Background reading

The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.

Ricci solitons Metrics that change under Ricci flow only by scaling and diffeomorphisms: shrinking, steady or expanding solitons. Start with: The Ricci flow on surfaces (Hamilton, 1988) Einstein metrics Metrics whose Ricci curvature is a constant multiple of the metric. They are the fixed points of normalised Ricci flow, and the most natural metrics… Start with: On the ricci curvature of a compact kähler manifold and the complex monge‐ampére equation, I (Yau, 1978)

In the guidebook

  1. 11B.1
    Ricci SolitonsBook 11B · Solitons, Compactness and Singularities

    Self-similar solutions: the Gaussian, cylinders, the cigar and the Bryant soliton.

  2. 12B.2
    The Asymptotic Soliton and Three-Dimensional ShrinkersBook 12B · κ-Solutions and Surgery

    Perelman's Proposition 11.2 proved with Morgan and Tian: the reduced-length bounds on κ-solutions, the limit of rescalings, the equality case, and the classification of shrinking solitons in dimensions two and three.