Department of Mathematics, K. S. Saket P. G. College Ayodhya,
Amanigunj, Uttar Pradesh, India
The study of Differential geometry makes us aware of the potential applications of exploring non- linear aspects and non- trivial symmetries arising in various models of gravity, classical and quantum field theory and geometric mechanics. The basic idea of Finsler space came from the groundbreaking “habilitation” lecture of Riemann: uber die Hypothesis; Welch der Geometric zugrnde liegen (on the Hypothesis, which lie at the Foundations of Geometry). During the last thirty years, Finsler geometry has gone under remarkable developments. Specially, a lot of results from Riemannian manifolds have been extended for Finsler manifolds by the researchers from all over the world.Presently, Finsler geometry has found an abundance of applications in both Physics and its applications. Finsler geometry has its roots in various problems of Differential equations, Calculus of variations, Mechanics and Theoretical Physics. Such applications include not only has the traditional area of the general Relativity, but also the theory of Yang- Mills fielded non- linear sigma models, superstring theory and quantum gravity and Biology. In Biology there are a lot of Finsler metrics which are suitable to describe biological models like Protien structure, coral leaf ecology etc.
The applications of Finsler geometry in various fields of science and its pure impact on real life problems motivate researchers to do research in this beautiful area of mathematics. We have worked on several interesting and important topics of Finsler Geometry like generalized beta – change of Finsler spaces, projective motion of Finsler spaces, Hypersurface of Finsler space with generalized beta – change of Finsler metric, generalized beta – change with h- vector in special Finsler spaces, theory of four and five dimensional ch- symmetric Finsler space with constant unified main scalar, recurrent Wagner connection of Finsler space with mth – root metric . I am currently working on existence of generalized beta conformal change of Finsler metric with an h- vector and investigating more than five dimensional ch symmetric Finsler spaces with constant unified main scalar.
Aims and Scope:
Generalized Beta - Change
Generalized Beta- Conformal Change
Finsler Space, Miron Frame, Unified Main Scalar, Landsberg Space