Abstract
The present chapter gives a prototype for a Cartan-Hadamard manifold, so complete, with seminegative curvature, simply connected, namely the space of symmetric positive definite real matrices of a given dimension. The example is obtained by “bending” a flat euclidean space by an exponential map. The chapter is essentially elementary, and could be read after the reader is acquainted with Riemannian metrics.
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© 1999 Springer Science+Business Media New York
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Lang, S. (1999). An Example of Seminegative Curvature. In: Fundamentals of Differential Geometry. Graduate Texts in Mathematics, vol 191. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0541-8_12
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DOI: https://doi.org/10.1007/978-1-4612-0541-8_12
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6810-9
Online ISBN: 978-1-4612-0541-8
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