The volumes of small geodesic balls for a metric connection

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1. [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. Zbl0223.53034MR282313
2. [2] M. Berger and B. Gostiaux: Géometrie Différentielle. Armand Colin, Paris, 1972. Zbl0251.53001MR494180
3. [3] J. Bertrand, C.F. Diguet and V. Puiseux: Démonstration d'un théorème de Gauss. Journal de Mathématiques13 (1848) 80-90. 
4. [4] F.J. Flaherty: The volume of a tube in complex projective space. Illinois J. Math.16 (1972) 627-638. Zbl0248.53051MR315638
5. [5] A. Gray: The volume of a small geodesic ball of a Riemannian manifold. Michigan Math. J.20 (1973) 329-344. Zbl0279.58003MR339002
6. [6] A. Gray and L. Vanhecke: Riemannian geometry as determined by the volume of small geodesic balls. Acta Math.142 (1979) 157-198. Zbl0428.53017MR521460
7. [7] A. Gray and L. Vanhecke: The volumes of tubes about curves in a Riemannian manifold (to appear). Zbl0491.53035MR647431
8. [8] A. Gray and L. Vanhecke: The volumes of tubes in a Riemannian manifold (to appear). Zbl0511.53059MR706043
9. [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. Zbl0409.53048MR507455
10. [10] N. Hicks: Notes on Differential Geometry. Van Nostrand, New York, 1965. Zbl0132.15104MR179691
11. [11] H. Hotelling: Tubes and spheres in n-spaces, and a class of statistical problems. Amer. J. Math.61 (1939) 440-460. Zbl0020.38302MR1507387JFM65.0795.02
12. [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. Paris290 (1980) 379-381. Zbl0428.53018MR567534
13. [13] H.S. Ruse, A.G. Walker, T.J. Willmore: Harmonic Spaces. Edizioni Cremonese, Rome, 1961. Zbl0134.39202MR142062
14. [14] H. Vermeil: Notiz über das mittlere Krümmungsmass einer n-fach ausgedehnten Riemann'schen Mannigfaltigkeit. Akad. Wissen. Gottingen Nach. (1917) 334-344. Zbl46.1130.01JFM46.1130.01
15. [15] H. Weyl: On the volume of tubes. Amer. J. Math.61 (1939) 461-472. Zbl0021.35503MR1507388JFM65.0796.01
16. [16] H. Weyl: The Classical Groups. Princeton Univ. Press, Princeton, N.J., 1939. 
17. [17] R.A. Wolf: The volume of tubes in complex projective space. Trans. Amer. Math. Soc.157 (1971) 347-371. Zbl0241.53033MR281237
18. [18] K. Yano: On semi-symmetric metric connection. Rev. Roum. Math. Pures et Appl.XV (1970) 1579-1586. Zbl0213.48401MR275321

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