Precize Differential Geometry-I (P.U.)


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The entire subject matter has been arranged in a simple, systematic, graded, lucid and exhaustive manner to meet the various needs of all types of learners. Each chapter begins with definitions followed by theorems with complete proofs and solved problems so that the study leads to perfect clarity and understanding. A large number of notes and remarks have been added for a better understanding of the subject.


Tensors : Notations and Summation Convention, Transformation law for vectors, Cartesian tensors, Algebra of Cartesian tensors, Differentiation of Cartesian tensors, The metric tensor, Transformation of curvilinear coordinates, General tensors, Contravariant, Covariant derivative of a vector, Physical components, Christoffel symbol, Relation with the metric tensor, Covariant derivative of a tensor, Riemann – Christoffel curvature tensor.

Curves with Torsion : Tangent, Principal normal, Curvature, Binormal, Torsion, Serret-Frenet formulae, Locus of Center of curvature, Circle of curvature, Torsion of a curve, Involutes, Evolutes and Bertrand curves.

Envelopes and Developable Surfaces : Surfaces, Tangent plane, normal, Envelope, Edge of regression, Developable surfaces, Curvilinear coordinates on a surface: Fundamental Magnitudes.