Taiwanese Journal of Mathematics

ON SLANT SURFACES

Bang-Yen Chen

Full-text: Open access

Abstract

A slant immersion was introduced in [1] as an isometric immersion of a Riemannian manifold into an almost Hermitian manifold with constant Wirtinger angle. It is known that there exist ample examples of slant submanifolds; in particular, slant surfaces in complex-spaceforms. In this paper, we establish a sharp inequality for slant surfaces and determine the Riemannian structures of special slant surfaces in complexspace- forms. By applying the special forms of the Riemannian structures on special slant surfaces we prove that proper slant surfaces in C2 are minimal if and only if they are special slant. We also determine proper slant surfaces in complex-space-forms which satisfy the equality case of the inequality identically.

Article information

Source
Taiwanese J. Math., Volume 3, Number 2 (1999), 163-179.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500407091

Digital Object Identifier
doi:10.11650/twjm/1500407091

Mathematical Reviews number (MathSciNet)
MR1692852

Zentralblatt MATH identifier
1013.53038

Citation

Chen, Bang-Yen. ON SLANT SURFACES. Taiwanese J. Math. 3 (1999), no. 2, 163--179. doi:10.11650/twjm/1500407091. https://projecteuclid.org/euclid.twjm/1500407091


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