@article{ASNSP_1981_4_8_3_473_0,
author = {Abbena, E. and Gray, A. and Vanhecke, L.},
title = {Steiner's formula for the volume of a parallel hypersurface in a riemannian manifold},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {473--493},
year = {1981},
publisher = {Scuola normale superiore},
volume = {Ser. 4, 8},
number = {3},
mrnumber = {634858},
zbl = {0472.53056},
language = {en},
url = {https://www.numdam.org/item/ASNSP_1981_4_8_3_473_0/}
}
TY - JOUR AU - Abbena, E. AU - Gray, A. AU - Vanhecke, L. TI - Steiner's formula for the volume of a parallel hypersurface in a riemannian manifold JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 1981 SP - 473 EP - 493 VL - 8 IS - 3 PB - Scuola normale superiore UR - https://www.numdam.org/item/ASNSP_1981_4_8_3_473_0/ LA - en ID - ASNSP_1981_4_8_3_473_0 ER -
%0 Journal Article %A Abbena, E. %A Gray, A. %A Vanhecke, L. %T Steiner's formula for the volume of a parallel hypersurface in a riemannian manifold %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 1981 %P 473-493 %V 8 %N 3 %I Scuola normale superiore %U https://www.numdam.org/item/ASNSP_1981_4_8_3_473_0/ %G en %F ASNSP_1981_4_8_3_473_0
Abbena, E.; Gray, A.; Vanhecke, L. Steiner's formula for the volume of a parallel hypersurface in a riemannian manifold. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 8 (1981) no. 3, pp. 473-493. https://www.numdam.org/item/ASNSP_1981_4_8_3_473_0/
[AB] , Tensor calculus through differential geometry, Butterworths, London, 1965. | Zbl | MR
[AL1] , The Euler number of a Riemannian manifold, Amer. J. Math., 62 (1940), pp. 243-248. | Zbl | MR | JFM
[AL2] , Steiner's formula on a general Sn+1, Bull. Amer. Math. Soc., 54 (1948), pp. 128-135. | Zbl | MR
[AL3] , Global differential geometry of imbedded manifolds, Problemi di geometria differenziale in grande, C.I.M.E., Cremonese, Roma, 1958. | Zbl
[AW] - , The Gauss-Bonnet theorem for Riemannian polyhedra, Trans. Amer. Math. Soc., 53 (1943), pp. 101-129. | Zbl | MR
[BGM] - - , Le spectre d'une variété riemannienne, Lecture Notes in Mathematics, vol. 194, Springer-Verlag, 1971. | Zbl | MR
[BG] - , Géométrie Différentielle, Armand Colin, Paris, 1972. | Zbl | MR
[BDP] - - , Demonstration d'un théorème de Gauss, Journal de Mathématiques, 13 (1848), pp. 80-90.
[BS] , Manifolds all of whose geodesics are closed, Ergebnisse der Mathematik, vol. 93, Springer-Verlag, 1978. | Zbl | MR
[BC] - , Geometry of manifolds, Academic Press, 1964. | Zbl | MR
[BK] , Vorlesungen über Integratgeometrie, Deutscher Verlag der Wissenschaften, 1955. | Zbl | MR
[BR] - , Einführung in die Differentialgeometrie, Springer-Verlag, 1960. | Zbl | MR
[BF] - , Theorie der konvexen Körper, Ergebnisse der Mathematik, Springer-Verlag, 1934, Chelsea reprint, 1948. | Zbl | MR
[CH1] , On the kinematic formula in the Euclidean space of N dimensions, Amer. J. Math., 74 (1952), pp. 227-236. | Zbl | MR
[CH2] , On the kinematic formula in integral geometry, J. Math. Mech., 16 (1966), pp. 101-118. | Zbl | MR
[DC] , Differential geometry of curves and surfaces, Prentice Hall, 1978. | Zbl | MR
[ER] , Riemannian manifolds of constant curvature and growth functions of submanifolds, Michigan Math. J., 19 (1972), pp. 215-223. | Zbl | MR
[FD1] , Curvature measures, Trans. Amer. Math. Soc., 93 (1959), pp. 418-491. | Zbl | MR
[FD2] , Geometric Measure Theory, Springer-Verlag, 1969. | Zbl | MR
[FE] , Sopra i fenomeni che avvengono in vicinanza di una linea oraria, Atti R. Accad. Lincei Rend. Cl. Sci. Fis. Mat. Nat., 31 (1922), pp. 21-23, 51-52, 101-103. Also The collected works of E. Fermi, vol. 1, pp. 17-19, The University of Chicago Press, 1962. | JFM
[FI] , Le problème des isopérimètres sur les surfaces ouvertes à coubure positive, Comment. Math. Helv., 13 (1941), pp. 293-341. | Zbl | MR | JFM
[FL1] , The volume of a tube in complex projective space, Illinois J. Math., 16 (1972), pp. 627-638. | Zbl | MR
[FL2] , Curvature measures for piecewise linear manifolds, Bull. Amer. Math. Soc., 79 (1973), pp. 100-102. | Zbl | MR
[GR1] , Minimal varieties and almost Hermitian submanifolds, Mich. Math. J., 12 (1965), pp. 273-287. | Zbl | MR
[GR2] , A generalization of F. Schur's theorem, J. Math. Soc. Japan, 21 (1969), pp. 454-457. | Zbl | MR
[GR3] , Some relations between curvature and characteristic classes, Math. Ann., 184 (1970), pp. 257-267. | Zbl | MR
[GR4] , Weak holonomy groups, Math. Z., 123 (1971), pp. 290-300. | Zbl | MR
[GR5] , The volume of a small geodesic ball in a Riemannian manifold, Michigan Math. J., 20 (1973), pp. 329-344. | Zbl | MR
[GR6] , Comparison theorems for the volumes of tubes as generalizations of the Weyl tube formula, Topology (to appear). | Zbl | MR
[GV1] - , Riemannian geometry as determined by the volumes of small geodesic balls, Acta Math., 142 (1979), pp. 157-198. | Zbl | MR
[GV2] - , The volume of tubes about curves in a Riemannian manifold, Proc. London Math. Soc. (to appear). | Zbl | MR
[GV3] - , The volume of tubes in a Riemannian manifold, (to appear). | Zbl | MR
[GV4] - , Oppervlakten van geodetische cirkels op oppervlakken, Med. Konink. Acad. Wetensch. Lett. Schone Kunst. België Kl. Wetensch., 42, No. 1 (1980), pp. 1-17. | Zbl | MR
[GS] , Complex differential geometry and curvature integrals associated to singularities of complex analytic varieties, Duke Math. J., 45 (1978), pp. 427-512. | Zbl | MR
[GN1] , Polynomial estimates for Betti numbers of loop spaces of symmetric and close to symmetric Riemannian manifolds, Indiana Math. J., 20 (1971), pp. 717-731. | Zbl | MR
[GN2] , On characterization of Riemannian manifolds by growth of tubular neigborhoods, Proc. Amer. Math. Soc., 32 (1972), pp. 556-560. | Zbl | MR
[GU] , Differential geometry, McGraw Hill, 1963. | Zbl | MR
[HA1] , Die erweiterten Steinerschen Formeln für ebene und sphitrische Bereiche, Comment. Math. Helv., 18 (1945), pp. 59-72. | Zbl | MR
[HA2] , Inhaltsungleichungen für innere und äusere Parallelmengen, Experientia (Basel), 2 (1946), p. 490. | Zbl | MR
[HA3] , Über das volumen der Parallelmengen, Mitt. Naturforsch. Ges. Bern., N.F., 3 (1946), pp. 121-125. | Zbl | MR
[HA4] , Über die erweiterten Steinerschen Formeln für Parallelmengen, Rev. Mat. Hispano-Americana, 4a serie, 6 (1946), pp. 160-163. | Zbl | MR
[HA5] , Vorlesungen über Inhalt, Oberfläche und Isoperimetrie, Springer-Verlag, 1957. | Zbl | MR
[HS] - , Mathematisches Wörterbuch, Akademie-Verlag, B. G. Teubner, Berlin, 1967.
[HZ] , Über die Steinersche Formel für Parallelflächen, Abh. Math. Sem. Hansischen Univ., 15 (1943), pp. 59-72. | Zbl | MR
[HR1] , Riemannian manifolds of finite order, Bull. Amer. Math. Soc., 78 (1972), pp. 200-201. | Zbl | MR
[HR2] , A characterization of Riemannian manifolds of constant curvature, J. Differential Geometry, 8 (1973), pp. 103-106. | Zbl | MR
[HW] - , A characterization of two dimensional Riemannian manifolds of constant curvature, Michigan Math. J., 17 (1970), pp. 297-299. | Zbl | MR
[HO] , Tubes and spheres in n-space and a class of statistical problems, Amer. J. Math., 61 (1939), pp. 440-460. | Zbl | MR | JFM
[OH] , Eine verallgemeinerung der Steinerschen Formel, Math. Ann., 129 (1955), pp. 204-212. | Zbl | MR
[ON] , Elementary differential geometry, Academic Press, 1966. | Zbl | MR
[OS1] , The isoperimetric inequatity, Bull. Amer. Math. Soc., 84 (1978), pp. 1182-1238. | Zbl | MR
[OS2] , Bonnesen-style isoperimetric inequalities, Amer. Math. Monthly, 86 (1979), pp. 1-29. | Zbl | MR
[SA] , Integral geometry and geometric probability, Encyclopedia of Mathematics and its Applications, Addison Wesley, 1976. | Zbl | MR
[SP] , A comprehensive introduction to differential geometry, vol. 5, Publish or Perish, Boston, 1975. | Zbl
[STE] , Über parallele Flächen, Monatsbericht der Akademie der Wissenchaften zu Berlin (1840), pp. 114-118,Also Werke, vol. 2 (1882), pp. 171-176.
[SW] - , Differentialgeometrie und Faserbündel, Birkhäuser Verlag, 1972. | Zbl | MR
[VA1] , Sobre un teorema de Liouville y generalización de fórmulas de Steiner, Rev. Mat. Hispano-Americana, 4a serie, 6 (1946), pp. 3-8. | MR
[VA2] , Sobre fórmulas de Steiner para el área de una elipse, Rev. Geodésica, 6 (1947), pp. 425-431.
[VA3] , A generalization of Steiner's formula, Bull. Amer. Math. Soc., 53 (1947), pp. 841-844. | Zbl | MR
[VA4] , Extensión del concepto de curvas paralelas sobre una superficie. Longitud y área correspondientes a la curvatura así deducida de otra dada, Rev. Math. Hispano-Americana, 4a serie, 7 (1947), pp. 3-12.
[VA5] , Area engendrada sobre una superficie por un arco de geodésica cuando uno de sus extremos recorre una curva fija y longitud de la curva descrita por el otro extremo, Rev. Mat. Hispano-Americana, 4a serie, 7 (1947), pp. 132-142. | MR
[VA6] , Curvas paralelas sobre superficies de curvatura constante, Rev. Union Math. Argentina, 8 (1948), pp. 135-138. | Zbl | MR
[VA7] , Introducción a la geometría diferencial, Dossat, Madrid, 1956. | Zbl | MR
[VA8] , Nueva deducción de las fórmulas de Steiner en un general Sn+1, Collectanea Mathematica, 14 (1962), pp. 47-50. | Zbl | MR
[WY] , On the volume of tubes, Amer. J. Math., 61 (1939), pp. 461-472. | Zbl | MR | JFM
[WO] , The volume of tubes in complex projective space, Trans. Amer. Math. Soc., 157 (1971), pp. 347-371. | Zbl | MR
[WU] , A characteristic property of the Euclidean plane, Michigan Math. J., 16 (1969), pp. 141-148. | Zbl | MR






