Some Metric Transformations on Finsler Spaces

Abstract

The present thesis entitled Some metric transformations on Finsler newlinespaces is the research work done during the previous years at Guru newlineGhasidas Vishwavidyalaya, Koni Bilaspur (C.G.). The thesis is divided newlineinto seven chapters and each chapter contains several sections. The dec newlineimal notation has been employed for numbering the equations. Refer newlineences to the equations are of the form (C.S.E.), where C, S, and E stand newlinefor the corresponding chapter, section, and equation respectively. The newlinenumbers in the square brackets refer to the references given at the end. newlineThe partial differential operators concerning xi and yi have been denoted newlineby and#8706;i and and#729;and#8706;i respectively. The notation j/k stands for the interchange of newlineindices j and k. newlineThe first chapter of the present thesis is introductory. The basic con newlinecepts and formulae from existing literature on Finsler spaces are given. newlineThese are useful for our discussion of subsequent chapters. newlineIn the second chapter, we study the Finsler space for the Matsumoto newlinechange with an h-vector . We obtain some fundamental tensors for this newlinetransformation. We also find the necessary and sufficient condition for newlinewhich the Cartan connection coefficients are invariant relative to the newlinechange. We have derived certain geometric properties of v-curvature newlinetensor for such change. We have also obtained the T-tensor for the newlinetransformed sapce and studied the Finsler space with Tand#8242;-condition and newlinesemi-Tand#8242;-condition. Chapter 3 introduces a conformal-Matsumoto change of the class of m newlineth root Finsler metrics. We have established the necessary and sufficient newlinecondition for the transformed metric to be projectively flat or locally newlinedually flat. Further, we have proved the non-existence of the concerned newlinemetric which is projectively flat with non-zero flag curvature. newlineIn chapter 4, we have considered the Finsler space Fn(n gt 2) with newlinea Generalized Matsumoto metric and found the necessary and sufficient newlinecriteria for it to be of Douglas type. We have also demonstrated the con newlinedition for the mentioned metric in Finsler space to