Nicoleta Aldea: On holomorphic curvature of $\eta$ - Einstein complex Finsler spaces, p.265-277

Abstract:

This paper comprises a class of complex Finsler metrics, namely $\eta -$ Einstein, which satisfies some special conditions on the curvature. By means of Chern complex linear connection on the pull-back tangent bundle, a special approach is devoted to obtain the equivalence conditions that a complex Finsler space should be $\eta -$ Einstein, (§3). A Schur type theorem for a $\eta -$ Einstein complex Finsler space, weakly Kähler, and other characterizations of the holomorphic curvature of this space are given in §4.

Key Words: Chern $(c.l.c)$, $\eta$ - Einstein space, constant curvature.

2000 Mathematics Subject Classification: Primary: 53C56,
Secondary: 53C60.

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