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Transformacións xeodésicas en xeometría cuaterniónica

por Fernández López, Manuel

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The notion of a re°ection with respect to a point or a linear subspace of the Euclideanspace has been generalized to that of a geodesic re°ection with respect to a point or asubmanifold in Riemannian manifolds. These local transformations have been broadlystudied not only in the general case but also in the framework of Hermitian, quaternionicand contact geometry. In many cases, this study leads to nice geometric properties andto characterizations of special classes of Riemannian manifolds or of special classes ofsubmanifolds (see, e.g., [CV1], [KPV], [TV] and [V]). In all these studies Jacobi vector¯elds and normal and Fermi coordinates are basic tools. Among other properties of thegeodesic re°ections isometric, volume-preserving, holomorphic, symplectic and harmonicones received special attention.


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The notion of a re°ection with respect to a point or a linear subspace of the Euclideanspace has been generalized to that of a geodesic re°ection with respect to a point or asubmanifold in Riemannian manifolds. These local transformations have been broadlystudied not only in the general case but also in the framework of Hermitian, quaternionicand contact geometry. In many cases, this study leads to nice geometric properties andto characterizations of special classes of Riemannian manifolds or of special classes ofsubmanifolds (see, e.g., [CV1], [KPV], [TV] and [V]). In all these studies Jacobi vector¯elds and normal and Fermi coordinates are basic tools. Among other properties of thegeodesic re°ections isometric, volume-preserving, holomorphic, symplectic and harmonicones received special attention.


  • Formato: PDF
  • Tamaño: 514 Kb.
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