Orthogonality preserving transformations on complex projective spaces

It is well known that transformations of $ \mathbb{C}^n $ preserving the standard inner product are unitary transformations. In this paper, all bijective transformations of isotropic sets of $ \mathbb{C}P^{n} $ preserving $ H $-orthogonality in both directions, called $ H $-orthogonal transformation...

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Bibliographic Details
Published inAIMS mathematics Vol. 10; no. 5; pp. 11411 - 11434
Main Authors Zhou, Kai, Gu, Zhenhua, Wu, Hongfeng
Format Journal Article
LanguageEnglish
Published AIMS Press 01.05.2025
Subjects
h-orthogonal
isotropic vector
orthogonality preserving
unitary group
wigner theorem
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ISSN2473-6988
2473-6988
DOI10.3934/math.2025519

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Summary:It is well known that transformations of $ \mathbb{C}^n $ preserving the standard inner product are unitary transformations. In this paper, all bijective transformations of isotropic sets of $ \mathbb{C}P^{n} $ preserving $ H $-orthogonality in both directions, called $ H $-orthogonal transformations, have been determined. This is a generalization of Uhlhorn's version of Wigner's unitary-antiunitary theorem. The group of $ H $-orthogonal transformations on some other sets of $ \mathbb{C}P^{n} $ were also determined.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2025519