Statistical submanifolds from a viewpoint of the Euler inequality

Statistical submanifolds from a viewpoint of the Euler inequality

We generalize the Euler inequality for statistical submanifolds. Several basic examples of doubly autoparallel statistical submanifolds in warped product spaces are described, for which the equality holds at each point. Besides, doubly totally-umbilical submanifolds are also illustrated.

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Veröffentlicht in:Information geometry 2021-07, Vol.4 (1), p.189-213
Hauptverfasser: Satoh, Naoto, Furuhata, Hitoshi, Hasegawa, Izumi, Nakane, Toshiyuki, Okuyama, Yukihiko, Sato, Kimitake, Shahid, Mohammad Hasan, Siddiqui, Aliya Naaz
Format: Artikel
Sprache:eng
Schlagworte:
Differential Geometry
Mathematics
Mathematics and Statistics
Research Paper
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Zusammenfassung:We generalize the Euler inequality for statistical submanifolds. Several basic examples of doubly autoparallel statistical submanifolds in warped product spaces are described, for which the equality holds at each point. Besides, doubly totally-umbilical submanifolds are also illustrated.
ISSN:2511-2481
2511-249X
DOI:10.1007/s41884-020-00032-4