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Circularm-functions

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Abstract

Circularm-functions are introduced on smooth manifolds with boundary. We study the distribution of their critical circles and construct an example of a four-dimensional manifoldM 4 with boundary ∂M 4 that satisfies the condition ξ(∂M 4)=ξ(M 4,∂M 4)=0 but does not contain any circularm-function. We prove that a manifold with boundaryM n (n≥5) such that ξ(∂M n, ∂M n)=0 always contains a circularm-function without critical points in the interior manifold.

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Authors
  1. T. A. Kurashvili
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Additional information

Sukhumi Branch of the Tbilisi University, Sukhumi. Translated from Ukrainskii Matermaticheskii Zhurnal, Vol. 46, No. 6, pp. 776–781, June, 1994.

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Kurashvili, T.A. Circularm-functions. Ukr Math J 46, 847–852 (1994). https://doi.org/10.1007/BF02658187

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  • DOI: https://doi.org/10.1007/BF02658187

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