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On the number of critical submanifolds of a function on a manifold

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Abstract

We consider differentiable functions on a manifold such that the set of their critical points is a disconnected union of smooth submanifolds. A topological characteristic of the manifold is introduced; in terms of this characteristic, we estimate the least possible number of critical submanifolds of these functions.

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Authors and Affiliations

  1. Kiev University, Kiev

    O. P. Bondar'

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  1. O. P. Bondar'
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 12, pp. 1702–1705, December, 1993.

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Bondar', O.P. On the number of critical submanifolds of a function on a manifold. Ukr Math J 45, 1915–1919 (1993). https://doi.org/10.1007/BF01061362

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  • DOI: https://doi.org/10.1007/BF01061362

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