Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
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Commun. Korean Math. Soc. 2012; 27(1): 197-200

Printed March 1, 2012

https://doi.org/10.4134/CKMS.2012.27.1.197

Copyright © The Korean Mathematical Society.

A note on compact almost K\"ahler locally symmetric spaces

Jaeman Kim

Kangwon National University

Abstract

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Concerning the integrability of almost K\"ahler manifolds, we prove that a compact almost K\"ahler locally symmetric space is K\"ahler if the length of the star Ricci tensor is not smaller than that of the Ricci tensor.

Keywords: integrability of almost K\"ahler manifoldsmanifolds, compact almost K\"ahler locally symmetric space, K\"ahler, the length of the star Ricci tensor, the length of the Ricci tensor

MSC numbers: 53A30, 53B35, 53C25, 53C55, 53C56

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