This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
A. Allamigeon, Propriétés globales des espaces de Riemann harmoniques, Ann. Inst. Fourier 15, 91–132 (1965).
A. Besse, Manifolds all of whose geodesics are closed, Ergebnisse der Mathematik, Bd. 93. Berlin, Heidelberg, New York, Springer 1978.
J. Cheeger and S. T. Yau, A Lower bound for the heat kernel, Comm. Pure and Applied Math. 34, 465–480 (1981).
B.-Y. Chen and P. Verheyen, Sous-variétés dont les sections normales sont des géodésiques, C. R. Acad. Sci. Paris Sér. A293, 611–613 (1981).
B.-Y. Ghen and P. Verheyen, Submanifolds with geodesic normal sections, Math. Ann. 269, 417–429 (1984).
R. Escobales, Riemannian submersions with totally geodesic fibers, J. Differential Geometry 10, 253–276 (1978).
D. Ferus, Symmetric submanifolds of Euclidean space, Math. Ann. 247, 81–93 (1980).
D. Ferus and S. Schirrmacher, Submanifolds in Euclidean space with simple geodesics, Math. Ann. 260, 57–62 (1982).
S. L. Hong, Isometric immersions of manifolds with plane geodesics into Euclidean space, J. Differential Geometry 8, 259–278 (1973).
Y. Komatsu, Special functions, in Japanese, Asakura, 1967.
J. A. Little, Manifolds with planar geodesics, J. Differential Geometry 11, 265–285 (1976).
K. Mashimo, Order of the standard isometric immersions of CROSS as helical geodesic immersions, Tsukuba J. Math. 7, 257–263 (1983).
D. Michel, Comparison des notions de variétés Riemanniennes globalement harmoniques et fortement harmoniques, C. R. Acad. Sci. Paris, Ser. A282, 1007–1010 (1976).
H. Nakagawa, On a certain minimal immersion of a Riemannian manifold into a sphere, Kodai Math. J. 3, 321–340 (1980).
H. S. Ruse, A. G. Walker and T. J. Willmore, Harmonic spaces, Consiglio Nacionale delle Ricerche Monographie Mathematiche 8, Roma, Edizioni Cremonese 1961.
K. Sakamoto, Planar geodesic immersions, Tohoku Math. J. 29, 25–56 (1977).
K. Sakamoto, Helical immersions into a unit sphere, Math. Ann. 261, 63–80 (1982).
K. Sakamoto, On a minimal helical immersion into a unit sphere, Advanced Studies in Pure Math. 3, 193–211 (1984).
K. Sakamoto, Helical minimal immersions of compact Riemannian manifolds into a unit sphere, Trans. Amer. Math. Soc. 288, 765–790 (1985).
K. Sakamoto, Helical minimal imbeddings of order 4 into spheres, J. Math. Soc. Japan 37, 315–336 (1985).
K. Sakamoto, The order of helical minimal imbeddings of strongly harmonic manifolds, to appear in Math. Z.
K. Sakamoto, Helical immersions into a Euclidean space, to appear in Michigan Math. J.
T. Takahashi, Minimal immersions of Riemannian manifolds, J. Math. Soc. Japan 18, 203–215 (1968).
F. G. Tricomi, Vorlesungen über orthogonal reihen, Springer, 1955.
K. Tsukada, Helical geodesic immersions of compact rank one symmetric spaces into spheres, Tokyo J. Math. 6, 267–285 (1983).
P. Verheyen, Submanifolds with geodesic normal sections are helical, to appear in Rendiconto del Seminario Mathematics dell' reniversita e del Politecmico di Torino.
N. R. Wallach, Minimal immersions of Riemannian manifolds, Symmetric spaces, edited by W. M. Boothby and G. L. Weiss, M. Dekker, New York, 1972.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1986 Springer-Verlag
About this paper
Cite this paper
Sakamoto, K. (1986). Helical immersions. In: Shiohama, K., Sakai, T., Sunada, T. (eds) Curvature and Topology of Riemannian Manifolds. Lecture Notes in Mathematics, vol 1201. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0075659
Download citation
DOI: https://doi.org/10.1007/BFb0075659
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16770-9
Online ISBN: 978-3-540-38827-2
eBook Packages: Springer Book Archive