Lectures on Tensor Calculus and Differential Geometry |
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Page 79
Johan Gerretsen. As a consequence there are functions § , § such that 1 r Γ ( 6.2-31 ) a = x ( s ) + Σ υ ξ . h = 1 h h ... consequence this vector function is a constant vector a . In addition we may infer from ( 6.2–29 ) that r i.e. , Σε ...
Johan Gerretsen. As a consequence there are functions § , § such that 1 r Γ ( 6.2-31 ) a = x ( s ) + Σ υ ξ . h = 1 h h ... consequence this vector function is a constant vector a . In addition we may infer from ( 6.2–29 ) that r i.e. , Σε ...
Page 133
... consequence , ẞ is the reciprocal of a principal curvature . Thus we see : The function ( 8.1–21 ) represents a hypersurface if and only if 1 / ẞ is not a principal curvature . The hypersurfaces x and x are called equidistant or ...
... consequence , ẞ is the reciprocal of a principal curvature . Thus we see : The function ( 8.1–21 ) represents a hypersurface if and only if 1 / ẞ is not a principal curvature . The hypersurfaces x and x are called equidistant or ...
Page 186
... consequence of ( 10.2-5 ) in the case that n > 2. In fact , applying Bianchi's identity ( 9.2-13 ) to ( 10.2-5 ) we get - V V λ = 0 . Contraction with respect to κ and v yields ( n − 2 ) ( Tur - Tru ) and this proves the assertion ...
... consequence of ( 10.2-5 ) in the case that n > 2. In fact , applying Bianchi's identity ( 9.2-13 ) to ( 10.2-5 ) we get - V V λ = 0 . Contraction with respect to κ and v yields ( n − 2 ) ( Tur - Tru ) and this proves the assertion ...
Contents
LINEAR VECTOR SPACES | 1 |
METRIC VECTOR SPACES | 14 |
BILINEAR AND QUADRATIC FORMS | 26 |
Copyright | |
15 other sections not shown
Common terms and phrases
angle arc length basis bivector called Christoffel symbols conditions of integrability congruence consider constant Riemannian curvature coordinate vector corresponding cos² covariant components covariant differentiation curve x(s denote differential equations dimension eigenvalues eigenvector expression finite dimensional follows geodesic curve given curve given point h h+1 h=1 h h Hence hyperplane hypersphere hypersurface identically line of curvature linear operator linearly independent metric space metric tensor metric vector space multilinear form multiplying both members n-dimensional normal number space obtained orthogonal orthonormal frame osculating parameter point space principal curvatures principal directions prove replace respect Riccian Riemannian curvature scalar invariant second fundamental tensor subspace symmetric taking account tangent space tangent vector tensor of valency theorem transformation Transvecting uniquely determined unit vector values vanishes vector function vector space zero vector βλ βλμ βμ Καβλμ νμ Σ σ Χλμ