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Abstract <p>The paper is devoted to the problem of local diagonalizability for pairs of quadratic differential forms depending on two real variables, which naturally generalizes the similar problem for algebraic quadratic forms. Here we have a new obstacle for diagonalization, which appears if a linear combination of the forms has an umbilic point, where all coefficients vanish simultaneously. The problem of local diagonalizability for single quadratic differential forms at umbilic points is also investigated.</p>

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Diagonalization of a Pair of Quadratic Differential Forms

  • 期刊论文

  • 发表日期：

    2025年2月1日

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  • A. S. Nikachev,
  • A. O. Remizov

摘要

Abstract

The paper is devoted to the problem of local diagonalizability for pairs of quadratic differential forms depending on two real variables, which naturally generalizes the similar problem for algebraic quadratic forms. Here we have a new obstacle for diagonalization, which appears if a linear combination of the forms has an umbilic point, where all coefficients vanish simultaneously. The problem of local diagonalizability for single quadratic differential forms at umbilic points is also investigated.