Abstract
In this chapter, we first recall the structure of indefinite quaternion Käahler manifolds. Then, we give a review of Riemannian submanifolds of quaternion Käahler manifolds. We study the geometry of real lightlike hypersurfaces, the structure of lightlike submanifolds, both, of indefinite quaternion Kähler manifolds and show that a quaternion lightlike submanifold is always totally geodesic. This result implies that the study of lightlike submanifolds, other than quaternion lightlike submanifolds, is interesting. Then, we deal with the geometry of screen real submanifolds in detail. As a generalization of real lightlike hypersurfaces of quaternion Kähler manifolds, we introduce QR-lightlike submanifolds. We show that the class of QR-lightlike submanifolds does not include quaternion lightlike submanifolds and screen real submanifolds. Then, we introduce and study the geometry of screen QR-lightlike and screen CR-lightlike submanifolds as generalizations of quaternion lightlike submanifolds and screen real submanifolds, and provide examples for each class of lightlike submanifolds of indefinite quaternion Kähler manifolds.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Rights and permissions
Copyright information
© 2010 Birkhäuser Verlag AG
About this chapter
Cite this chapter
(2010). Submanifolds of indefinite quaternion Kähler manifolds. In: Differential Geometry of Lightlike Submanifolds. Frontiers in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0251-8_8
Download citation
DOI: https://doi.org/10.1007/978-3-0346-0251-8_8
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0346-0250-1
Online ISBN: 978-3-0346-0251-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)