Characterizations of space forms by circles on their geodesic spheres. (English) Zbl 1030.53057

Starting from the previous work of the authors [Bull. Aust. Math. Soc. 62, No. 2, 205-210 (2000; Zbl 0978.53071)] where the space forms are characterized in terms of the extrinsic shape of geodesics in geodesic spheres, in this paper, the authors extend the obtained results by using circles on their geodesic spheres.
Reviewer: V.Cruceanu (Iaşi)


53C40 Global submanifolds
53B25 Local submanifolds


Zbl 0978.53071
Full Text: DOI


[1] Adachi, T., and Maeda, S.: Space forms from the viewpoint of their geodesic spheres. Bull. Austral. Math. Soc., 62 , 205-210 (2000). · Zbl 0978.53071
[2] Adachi, T., Maeda, S., and Udagawa, S.: Circles in a complex projective space. Osaka J. Math., 32 , 709-719 (1995). · Zbl 0857.53034
[3] Chen, B.-Y., and Vanhecke, L.: Differential geometry of geodesic spheres. J. Reine Angew. Math., 325 , 28-67 (1981). · Zbl 0503.53013
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