Salah Elgendi

Generalized Beta Conformal Changes: General Theory of (,)-metric with Applications to Special Finsler Spaces Salah Elgendi

Transformations or changes of Finsler metrics have many applications not only in differential geometry but also in various branches of science, especially in physics. These changes have been studied by many authors, from both the mathematical and physical aspects. G. Randers, in 1941, introduced the Randers change. M. Masumoto, in 1974, studied the Randers change and generalized Randers change. V. Kropina, in 1961, introduced the Kropina change. On the other hand, in 1976, M. Hashiguchi studied the conformal change of Finsler metrics. In 2008, S. Abed introduced the ?-conformal change, thus generalizing the conformal, Randers and generalized Randers changes. In this work, we introduce a more general change of Finsler metrics, which is referred to as a generalized ?-conformal change. This change combines both ?-change and conformal change, in a general setting, generalizing the most important changes existing in the literature. The geometric consequences of such change are investigated. Various special Finsler spaces are studied under this change. This book is highly recommended to both postgraduate students and researchers in geometry and its applications, especially in physics.