Totally geodesic surfaces in the complex quadric

Autor:	Marilena Moruz, Joeri Van der Veken, Luc Vrancken, Anne Wijffels
Rok vydání:	2022
Předmět:	Mathematics::Algebraic Geometry Mathematics::Commutative Algebra Mathematics::Differential Geometry
Zdroj:	Differential Geometry and Global Analysis. :153-161
ISSN:	1098-3627 0271-4132
DOI:	10.1090/conm/777/15633
Popis:	We provide explicit descriptions of all totally geodesic surfaces of a complex quadric of arbitrary dimension. Totally geodesic submanifolds of complex quadrics were first studied by Chen and Nagano in 1977 and fully classified by Klein in 2008. In particular, we interpret some of these surfaces as Gaussian images of surfaces in a unit three-sphere and all others as elements of the Veronese sequence introduced by Bolton, Jensen, Rigoli and Woodward. We also briefly discuss how the classification can be translated to the non-compact dual of the complex quadric, namely the hyperbolic complex quadric.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::39820b83d92851a40995bea955d79ecf https://doi.org/10.1090/conm/777/15633 Zobrazit plný text záznamu