한국수학교육학회지시리즈B:순수및응용수학 (The Pure and Applied Mathematics)

  • 제5권1호
  • /
  • Pages.55-63
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  • 1998
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  • 1226-0657(pISSN)
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  • 2287-6081(eISSN)
한국수학교육학회 (Korean Society of Mathematical Education)
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HARMONIC GAUSS MAP AND HOPF FIBRATIONS

  • 발행 : 1998.05.01
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초록

A Gauss map of m-dimensional distribution on a Riemannian manifold M is called a harmonic Gauss map if it is a harmonic map from the manifold into its Grassmann bundle $G_m$(TM) of m-dimensional tangent subspace. We calculate the tension field of the Gauss map of m-dimensional distribution and especially show that the Hopf fibrations on $S^{4n＋3}$ are the harmonic Gauss map of 3-dimensional distribution.

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