Non-existence of conformally flat real hypersurfaces in both the complex quadric and the complex hyperbolic quadric

Yao, Zeke; Yin, Bangchao; Hu, Zejun

doi:10.4153/s0008439521000084

Cited by 5 publications

(2 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The method used in the proof of Lemma 4.1 is called the Tsinghua principle. This remarkable technique has been applied in many different situations since its first successful attempt in [1], see [5,6,13,14,21,22] for details.…”

Section: Proofs Of Theorem 11 and Theorem 12mentioning

confidence: 99%

See 1 more Smart Citation

Affine hypersurfaces with constant sectional curvature

Antić

Vrancken

et al. 2021

Pacific J. Math.

View full text Add to dashboard Cite

In this paper, we classify the hypersurfaces of S 2 × S 2 with constant sectional curvature. By applying the so-called Tsinghua principle, which was first discovered by the first three authors in 2013 at Tsinghua University, we prove that the constant sectional curvature can only be 1 2 and the product angle function C defined by Urbano is identically zero. We show that any such hypersurface is a parallel hypersurface of a minimal hypersurface in S 2 × S 2 with C = 0, and we establish a one-to-one correspondence between the involving minimal hypersurface and the famous "sinh-Gordon equation"As a byproduct, we give a complete classification of the hypersurfaces of S 2 × S 2 with constant mean curvature and constant product angle function C.

show abstract

Section: Proofs Of Theorem 11 and Theorem 12mentioning

confidence: 99%

“…By using such approach, some canonical submanifolds with constant sectional curvature (even under more general conditions) in some canonical Riemannian manifold have been classified, cf. [1,5,6,14,21,22], etc. The main purpose of this paper is to classify the hypersurfaces of S 2 × S 2 with constant sectional curvature.…”

Section: Introductionmentioning

confidence: 99%