By Krishan L. Duggal, Ramesh Sharma
This publication presents an upto date info on metric, connection and curva ture symmetries utilized in geometry and physics. extra particularly, we current the characterizations and classifications of Riemannian and Lorentzian manifolds (in specific, the spacetimes of basic relativity) admitting metric (i.e., Killing, ho mothetic and conformal), connection (i.e., affine conformal and projective) and curvature symmetries. Our method, during this e-book, has the subsequent amazing positive factors: (a) it's the first-ever test of a entire selection of the works of a really huge variety of researchers on all of the above pointed out symmetries. (b) we now have aimed toward bringing jointly the researchers attracted to differential geometry and the mathematical physics of normal relativity via giving an invariant in addition to the index kind of the most formulation and effects. (c) try has been made to aid numerous major mathematical effects through bringing up actual example(s) as utilized to basic relativity. (d) total the presentation is self contained, rather available and in a few exact instances supported by way of an in depth record of pointed out references. (e) the fabric coated may still stimulate destiny study on symmetries. Chapters 1 and a couple of comprise many of the necessities for interpreting the remainder of the booklet. We current the language of semi-Euclidean areas, manifolds, their tensor calculus; geometry of null curves, non-degenerate and degenerate (light like) hypersurfaces. All this can be defined in invariant in addition to the index form.