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This book combines the classical and contemporary approaches to
differential geometry. An introduction to the Riemannian geometry
of manifolds is preceded by a detailed discussion of properties of
curves and surfaces.The chapter on the differential geometry of
plane curves considers local and global properties of curves,
evolutes and involutes, and affine and projective differential
geometry. Various approaches to Gaussian curvature for surfaces are
discussed. The curvature tensor, conjugate points, and the
Laplace-Beltrami operator are first considered in detail for
two-dimensional surfaces, which facilitates studying them in the
many-dimensional case. A separate chapter is devoted to the
differential geometry of Lie groups.
This book combines the classical and contemporary approaches to
differential geometry. An introduction to the Riemannian geometry
of manifolds is preceded by a detailed discussion of properties of
curves and surfaces.The chapter on the differential geometry of
plane curves considers local and global properties of curves,
evolutes and involutes, and affine and projective differential
geometry. Various approaches to Gaussian curvature for surfaces are
discussed. The curvature tensor, conjugate points, and the
Laplace-Beltrami operator are first considered in detail for
two-dimensional surfaces, which facilitates studying them in the
many-dimensional case. A separate chapter is devoted to the
differential geometry of Lie groups.
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