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A differential equation related with some general connections

  • Tominosuke Otsuki
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 350)

Abstract

A general connection Γ on a differentiable manifold M n is given as a geometrical object with components (Pi jTi jh) in local coordinates (ui) such that (P i j ) are the components of a tensor and (Ti j) satisfy the rules : Γ< _ dv’ f p k g V M0vT\ Jh ~ duk \ 1 dvidvh + lmdvi dvh J ’ where T i j are the second components of Γ in local coordinates (vi). We call a point of M n is regular or singular with respect to Γ if det (P i j ) ≠ 0 or = 0, respectively. We say a curve γ(t) = (u i (t)) is a geodesic with respect to Γ if u i (t) satisfy the equations: ni d2v? „, du* duh „ and the parameter t is called its affine parameter.

Keywords

Scalar Curvature Galerkin Method Hyperbolic Space Ricci Tensor Nonlinear Partial Differential Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    T. Otsuki: General connections, Math. J. Okayama Univ. 32(1990), 227–242.MathSciNetzbMATHGoogle Scholar
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    T. Otsuki: Behavior of geodesies around the singular set of a general connection, SUT Journal of Math. 27(1991), 169–228.MathSciNetzbMATHGoogle Scholar
  3. 3.
    T. Otsuki: A family of Minkowski-type spaces with general connections, SUT J. Math. 28 (1992), 61–103.MathSciNetzbMATHGoogle Scholar
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    T. Otsuki: A nonlinear partial differential equation related with certain spaces with general connections, SUT J. Math. 29 (1993), 167–192.MathSciNetzbMATHGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Tominosuke Otsuki
    • 1
  1. 1.Department of MathematicsScience University of TokyoShinjuku-ku, Tokyo 162Japan

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