PORTUGALIAEMATHEMATICA
Vol. 58, No. 2, pp. 219-231 (2001)
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PORTUGALIAE MATHEMATICA Vol. 58, No. 2, pp. 219-231 (2001) |
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On Totally Real Submanifolds in A Nearly Kähler ManifoldZhong Hua HouDepartment of Applied Mathematics, Dalian University of Technology,Dalian 116024, Liaoning -- PEOPLE'S REPUBLIC OF CHINA E-mail: zhhou@dlut.edu.cn and CMAF, Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa -- PORTUGAL E-mail: zhhou@lmc.fc.ul.pt Abstract: Let $M^m$ be a totally real submanifold of a nearly Kähler manifold $\bar M^{2m}$. We prove an important relationship between the covariant differential of the second fundamental form of $M^m$ and that of the almost complex structure of $\bar M^{2m}$. And we show an application to the pinching problem on the square of the length of the second fundamental form of $M^m$. Keywords: Nearly Kähler manifold; Totally real submanifold. Classification (MSC2000): 53C42.; 32v40. Full text of the article:
Electronic version published on: 9 Feb 2006. This page was last modified: 27 Nov 2007.
© 2001 Sociedade Portuguesa de Matemática
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