Taiwanese Journal of Mathematics

ON SLANT SUBMANIFOLDS OF NEUTRAL KAEHLER MANIFOLDS

K. Arslan, A. Carriazo, B.-Y. Chen, and C. Murathan

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Abstract

An indefinite Riemannian manifold is called neutral it its index is equal to one half of its dimension and an indefinite Kaehler manifold is called neutral Kaehler if its complex index is equal to the half of its complex dimension. In the first part of this article, we extend the notion of slant surfaces in Lorentzian Kaehler surfaces to slant submanifolds in neutral Kaehler manifolds; moreover, we characterize slant submanifolds with parallel canonical structures. By applying the results obtained in the first part we completely classify slant surfaces with parallel mean curvature vector and minimal slant surfaces in the Lorentzian complex plane in the second part of this article.

Article information

Source
Taiwanese J. Math., Volume 14, Number 2 (2010), 561-584.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405807

Digital Object Identifier
doi:10.11650/twjm/1500405807

Mathematical Reviews number (MathSciNet)
MR2655787

Zentralblatt MATH identifier
1202.53022

Subjects
Primary: 53C40: Global submanifolds [See also 53B25]
Secondary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) [See also 49Q05, 49Q10, 53A10, 57R40, 57R42] 53B25: Local submanifolds [See also 53C40]

Keywords
slant submanifold neutral Kaehler manifold neutral complex space form minimal surface Lorentzian complex plane

Citation

Arslan, K.; Carriazo, A.; Chen, B.-Y.; Murathan, C. ON SLANT SUBMANIFOLDS OF NEUTRAL KAEHLER MANIFOLDS. Taiwanese J. Math. 14 (2010), no. 2, 561--584. doi:10.11650/twjm/1500405807. https://projecteuclid.org/euclid.twjm/1500405807


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