The volumes of small geodesic balls for a metric connection
Miquel, V.
Compositio Mathematica, Tome 47 (1982), p. 121-132 / Harvested from Numdam
Publié le : 1982-01-01
@article{CM_1982__46_1_121_0,
     author = {Miquel, V.},
     title = {The volumes of small geodesic balls for a metric connection},
     journal = {Compositio Mathematica},
     volume = {47},
     year = {1982},
     pages = {121-132},
     mrnumber = {660156},
     zbl = {0489.53043},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1982__46_1_121_0}
}
Miquel, V. The volumes of small geodesic balls for a metric connection. Compositio Mathematica, Tome 47 (1982) pp. 121-132. http://gdmltest.u-ga.fr/item/CM_1982__46_1_121_0/

[1] M. Berger, P. Gauduchon, and E. Mazet: Le spectre d'une variété riemannienne. Lecture Notes in Mathematics, vol. 194, Springer Verlag, Berlin and New York, 1971. | MR 282313 | Zbl 0223.53034

[2] M. Berger and B. Gostiaux: Géometrie Différentielle. Armand Colin, Paris, 1972. | MR 494180 | Zbl 0251.53001

[3] J. Bertrand, C.F. Diguet and V. Puiseux: Démonstration d'un théorème de Gauss. Journal de Mathématiques 13 (1848) 80-90.

[4] F.J. Flaherty: The volume of a tube in complex projective space. Illinois J. Math. 16 (1972) 627-638. | MR 315638 | Zbl 0248.53051

[5] A. Gray: The volume of a small geodesic ball of a Riemannian manifold. Michigan Math. J. 20 (1973) 329-344. | MR 339002 | Zbl 0279.58003

[6] A. Gray and L. Vanhecke: Riemannian geometry as determined by the volume of small geodesic balls. Acta Math. 142 (1979) 157-198. | MR 521460 | Zbl 0428.53017

[7] A. Gray and L. Vanhecke: The volumes of tubes about curves in a Riemannian manifold (to appear). | MR 647431 | Zbl 0491.53035

[8] A. Gray and L. Vanhecke: The volumes of tubes in a Riemannian manifold (to appear). | MR 706043 | Zbl 0511.53059

[9] P.A. Griffiths: Complex differential and integral geometry and curvature integrals associated to singularities of complex analytic varieties. Duke Math. J. 45 (1978) 427-512. | MR 507455 | Zbl 0409.53048

[10] N. Hicks: Notes on Differential Geometry. Van Nostrand, New York, 1965. | MR 179691 | Zbl 0132.15104

[11] H. Hotelling: Tubes and spheres in n-spaces, and a class of statistical problems. Amer. J. Math. 61 (1939) 440-460. | JFM 65.0795.02 | MR 1507387 | Zbl 0020.38302

[12] V. Miquel and A.M. Naveira: Sur la relation entre la fonction volume de certaines boules géodésiques et la géométrie d'une variété riemannienne. C.R. Acad. Sci. Paris 290 (1980) 379-381. | MR 567534 | Zbl 0428.53018

[13] H.S. Ruse, A.G. Walker, T.J. Willmore: Harmonic Spaces. Edizioni Cremonese, Rome, 1961. | MR 142062 | Zbl 0134.39202

[14] H. Vermeil: Notiz über das mittlere Krümmungsmass einer n-fach ausgedehnten Riemann'schen Mannigfaltigkeit. Akad. Wissen. Gottingen Nach. (1917) 334-344. | JFM 46.1130.01

[15] H. Weyl: On the volume of tubes. Amer. J. Math. 61 (1939) 461-472. | JFM 65.0796.01 | MR 1507388 | Zbl 0021.35503

[16] H. Weyl: The Classical Groups. Princeton Univ. Press, Princeton, N.J., 1939.

[17] R.A. Wolf: The volume of tubes in complex projective space. Trans. Amer. Math. Soc. 157 (1971) 347-371. | MR 281237 | Zbl 0241.53033

[18] K. Yano: On semi-symmetric metric connection. Rev. Roum. Math. Pures et Appl. XV (1970) 1579-1586. | MR 275321 | Zbl 0213.48401