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Differential Geometry of Curves and Surfaces in E3 (Tensor Approach) de Uday Chand De

Differential Geometry of Curves and Surfaces in E3 (Tensor Approach)

Autor Uday Chand De
en Limba Engleză Hardback – 30 apr 2007
Helps overcome the difficulties in understanding the underlying concepts of the subject. This book introduces the methodology of differential geometry to research students in associated disciplines of physics, engineering, biosciences and economics. It concludes with a brief history of differential geometry.
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Specificații

ISBN-13: 9781905740543
ISBN-10: 1905740549
Pagini: 190
Ediția:New.
Editura: ANSHAN PUB

Notă biografică

Uday Chand De Dept of Mathematics University of Kalyani, India

Cuprins

1. CURVILINEAR COORDINATES 1.1Curvilinear Coordinate System in E3 1.2 Elementary Arc Length 1.3 Length of a Vector 1.4 Angle betweenTwo Non-null Vectors 1.5 Reciprocal Base System 1.6 On the Meaning of Covariant Derivatives 1.7 Intrinsic Differentiation 1.8 Parallel Vector Fields 2. GEOMETRY OF SPACE CURVES 2.1 Serret-Frenet Formulae 2.2 Equation of a Straight Line in Curvilinear Coordinate system 2.3 Some Results on Curvature and Torsion. How to Find out Curvature and Torsion of Space Curves 2.4 Helix 3. INTRINSIC GEOMETRY OF A SURFACE 3.1 Curvilinear Coordinates of a Surface 3.2 The Element of Length and the Metric Tensor 3.3 The First Fundamental Form 3.4 Directions on a Surface. Angle between Two Directions 3.5 Geodesic and its Equations 3.6 Parallelism with respect to a Surface 3.7 Intrinsic and Covariant Differentiation of Surface Tensors 3.8 The Riemann-Christoffel Tensor. The Gaussian Curvature of a Surface 3.9 The Geodesic Curvature of a Curve on a Surface 4. THE FUNDAMENTAL FORMULAE OF A SURFACE 4.1 The Tangent Vector to a Surface 4.2 The Normal Vector to a Surface 4.3 The Tensor Derivation of Tensors 4.4 Gauss's Formulae: The second Fundamental Form of a Surface 4.5 Weingarten's Formulae: The Third Fundamental Form of a Surface 4.5 The Equations of Gauss and Codazzi 5. CURVES ON A SURFACE 5.1 The Equations of a Curve on a Surface 5.2 Meusnier's Theorem 5.3 The principal curvatures 5.4 The Lines of Curvature 5.5 The Asymptotic Lines. Enneper's Formula 5.6 The Geodesic Torsion of a Curve on a Surface