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THE MINIMAL $S^{3}$ WITH CONSTANT SECTIONAL CURVATURE IN $\mathit{CP}^{n}$

Part of: Global differential geometry

Published online by Cambridge University Press:  18 February 2015

SEN HU  and
KANG LI
SEN HU
Affiliation:
School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, Anhui, China Wu Wen-Tsun Key Laboratory of Mathematics, USTC, Chinese Academy of Sciences, Hefei 230026, Anhui, China email [email protected]
KANG LI*
Affiliation:
School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, Anhui, China email [email protected]
*
✉[email protected]
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Abstract

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It is known that the minimal 3-spheres of CR type with constant sectional curvature have been classified explicitly, and also that the weakly Lagrangian case has been studied. In this paper, we provide some examples of minimal 3-spheres with constant curvature in the complex projective space, which are neither of CR type nor weakly Lagrangian, and give the adapted frame of a minimal 3-sphere of CR type with constant sectional curvature.

Keywords

minimalconstant sectional curvatureCR typeweakly Lagrangian

MSC classification

Primary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.)
Secondary: 53C55: Hermitian and Kählerian manifolds
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 99 , Issue 1 , August 2015 , pp. 63 - 75
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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