Diagonalization of a Pair of Quadratic Differential Forms

Author(s)

Nikachev, A. S. ; Remizov, A. O.

• Document type: Journal article
• Source: LOBACHEVSKII JOURNAL OF MATHEMATICS; v. 46, n. 2, p. 8-pg., 2025-02-01.

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. (AU)

• FAPESP's process: 19/07316-0 - Singularity theory and its applications to differential geometry, differential equations and computer vision
• Grantee: Farid Tari
• Support Opportunities: Research Projects - Thematic Grants