On Holomorphic Curvature of Complex Finsler Square Metric

Sarathi Mallappa Vanithalakshmi,Mallappa Kariyappa Roopa,Senajji Kampalappa Narasimhamurhthy

doi:10.4236/apm.2019.99035

Abstract

The notion of the holomorphic curvature for a Complex Finsler space (M,F) is defined with respect to the Chern complex linear connection on the pull-back tangent bundle. This paper is about the fundamental metric tensor, inverse tensor and as a special approach of the pull-back bundle is devoted to obtaining the holomorphic curvature of Complex Finsler Square metrics. Further, it proved that it is not a weakly Kahler.

Highlights

This paper is about the fundamental metric tensor, inverse tensor and as a special approach of the pull-back bundle is devoted to obtaining the holomorphic curvature of Complex Finsler Square metrics
The notion of holomorphic curvature of a complex Finsler space is defined with respect to the Chern complex linear connection in briefly Chern (c.l.c) as a connection in the holomorphic pull back tangent bundle π * (T ′M )
In [1], Nicolta Aldea has obtained the characterization of the holomorphic bisectional curvature and gave the generalization of the holomorphic curvature of the complex Finsler spaces which are called holomorphic flag curvature

Summary

Introduction

The notion of holomorphic curvature of a complex Finsler space is defined with respect to the Chern complex linear connection in briefly Chern (c.l.c) as a connection in the holomorphic pull back tangent bundle π * (T ′M ) (here π represented as projection). After that in (2006) he devoted to obtaining the characterization of holomorphic flag curvature. In complex Finsler geometry, it is systematically used the concept of holomorphic curvature in direction η. The holomorphic curvature is not an analogue of the flag curvature from real Finsler geometry. This problem sets up the subject of the present paper. Our goal is to determine the conditions in which complex Finsler spaces with square metric of holomorphic curvature. We determine the holomorphic curvature of complex square metric (theorem (4.3)) and some special properties of holomorphic curvature are obtained (proposition (4.4))

Preliminaries

Notation of Complex Square Metrics

Holomorphic Curvature of Complex Square Metric

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