Geodesic
Slant submanifolds ofcomplex projective and complex hyperbolic spaces
Glasgow mathematical journal, Tome 42 (2000) no. 3, pp. 439-454

Voir la notice de l'article provenant de la source Cambridge University Press

An interestingclass of submanifolds of Hermitian manifolds is the class of slant submanifolds which are submanifoldswith constant Wirtinger angle. In [1–4,7,8] slantsubmanifolds of complex projective and complex hyperbolic spaces have been investigated. Inparticular, it was shown that there exist many proper slant surfaces in CP^2 and inCH^2 and many proper slant minimal surfaces in C2. In contrast,in the first part of this paper we prove that there do not exist proper slant minimal surfaces inCP^2 and in CH^2. In the second part, we present a generalconstruction procedure for obtaining the explicit expressions of such slant submanifolds. By applyingthis general construction procedure, we determine the explicit expressions of special slant surfacesof CP^2 and of CH^2. Consequently, we are able to completelydetermine the slant surface which satisfies a basic equality. Finally, we apply the constructionprocedure to prove that special θ-slant isometric immersions of a hyperbolicplane into a complex hyperbolic plane are not unique in general. 
Chen, Bang-Yen; Tazawa, Yoshihiko. Slant submanifolds ofcomplex projective and complex hyperbolic spaces. Glasgow mathematical journal, Tome 42 (2000) no. 3, pp. 439-454. doi: 10.1017/S0017089500030111
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