Abstract
A submanidfold S of a Riemannian manifold is called a totally geodesic submanifold if every geodesic of S is also a geodesic of M. Totally geodesic submanifolds of Riemannian symmetric spaces have long been studied by many mathematicians. We give a classification of non-flat totally geodesic surfaces of the Riemannian symmetric space of type AI, AIII and BDI.
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References
Helgason, S.: Differential Geometry, Lie Groups, and Symmetric Spaces. Academic press, New York (1978)
Klein, S.: Totally Geodesic Submanifolds in Riemannian Symmetric Spaces. arXiv:0810.4413v1 [math.DG]
Mashimo, K.: Non-flat Totally Geodesic Surfaces in Symmetric Spaces of Classical Type. Preprint
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© 2014 Springer Japan
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Mashimo, K. (2014). Totally Geodesic Surfaces of Riemannian Symmetric Spaces. In: Suh, Y.J., Berndt, J., Ohnita, Y., Kim, B.H., Lee, H. (eds) Real and Complex Submanifolds. Springer Proceedings in Mathematics & Statistics, vol 106. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55215-4_26
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DOI: https://doi.org/10.1007/978-4-431-55215-4_26
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Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-55214-7
Online ISBN: 978-4-431-55215-4
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