On foliations with leaves satisfying some geometrical conditions

Walczak, Paweł Grzegorz

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On foliations with leaves satisfying some geometrical conditions

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Paweł Grzegorz Walczak

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Rozprawy Matematyczne tom/nr w serii: 226 wydano: 1983

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CONTENTS
Introduction.................................................5
1. Preliminaries...........................................6
1. A. Foliations...........................................7
1. B. Geometry of submanifolds.................9
2. The characteristic form..........................11
3. Stability of minimal foliations..................18
4. A metric on the space of foliations.........24
5. Jacobi fields on leaves..........................27
6. The Gauss mapping of a foliation.........37
References...............................................45

Słowa kluczowe

Tematy

Wydawca

Instytut Matematyczny Polskiej Akademii Nauk

Miejsce publikacji

Warszawa

Copyright

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Rozprawy Matematyczne tom/nr w serii: 226

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47

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Opis fizyczny

Dissertationes Mathematicae, Tom CCXXVI

Daty

wydano

1983

Twórcy

autor

Paweł Grzegorz Walczak

Bibliografia

[1] W. K. Allard, On the first variation of a varifold, Ann. of Math. 95 (1972), 417-491.
[2] W. K. Allard, F. J. A. Imgren, On thee radial behaviour of minimal surface and the uniqueness of their tangent cones, Ann. of Math. 113 (1981), 215-266.
[3] G. Andrzejczak, On some form determined by a distribution on a Riemannian manifold, Colloq. Math. 41 (1978), 79-83.
[4] R. L. Bishop, A relation between volume, mean curvature and diameter, Notices Amer. Math. Soc. 10 (1963), 364.
[5] R. L. Bishop, R. J. Crittenden, Geometry of Manifolds, Academic Press, New York, 1964.
[6] R. Bott, Lectures on characteristic classes and foliations, Lectures on Algebraic and Differential Topology, Lecture Notes in Math. 279, Springer Verlag, 1972, 1-94.
[7] R. Bott, H. Samelson, Applications of the theory of Morse to symmetric spaces, Amer. J. Math. 80 (1958), 964-1029.
[8] F. Brito, R. Langevin,H. Rosenberg, Intégrales de courbure des variétés feuilletées, C. R. Acad. Sci. Paris 285 (1977), A533-A536.
[9] D. Burns, Jacobi fields on complex cones, in preparation.
[10] L. S. Charlap, A. T. Vasquez, The cohomology of $Z_p$-manifolds, Amer. J. Math. 87 (1965), 551-563.
[11] B.-Y. Chen, Geometry of Submanifolds, Marcel Dekker, New York 1973.
[12] T. Duchamp, M. Kalka, Holomorphic foliations and the Kobayashi metric, Proc. Amer. Math. Soc. 67 (1977), 117-122.
[13] A. Duschek, Das Variazionsproblem der $F_m$ im Riemannschen $R_n$ und eine Verallgemeinerung des Gauss-Bonnetschen Satzes, Math. Z. 40 (1936), 279-291.
[14] R. D. Edwards, K. C. Millett, D. Sullivan, Foliations with all leaves compact, Topology 16 (1977), 13-32.
[15] J. Eells, L. Lemaire, A report on harmonic maps, Bull. London Math. Soc. 10 (1978), 1-68.
[16] J. Eells, J. H. Sampson, Harmonic mappings of Riemannian manifolds, Amer. J. Math. 86 (1964), 109-160.
[17] D. B. A. Epstein, Periodic flows on three-manifolds, Ann. of Math. 95 (1972), 66-82.
[18] D. B. A. Epstein, Foliations with all leaves compact, Ann. Inst. Fourier 26 (1976), 265-282.
[19] D. B. A. Epstein, A topology for the space of foliations, preprint, Warwick Univ., 1977.
[20] D. B. A. Epstein, K. C. Millett, D. Tischler, Leaves without holonomy, J. London Math. Soc. 16 (1977), 548-552.
[21] D. B. A. Epstein, E. Vogt, A counterexample to the Periodic Orbit Conjecture in codimension 3, Ann. of Math. 108 (1978), 539-552.
[22] R. H. Escobales, Riemannian submersions with totally geodesic fibres, J. Differential Geometry 10 (1975), 253-276.
[23] R. H. Escobales, Riemannian submersions from complex projective space, ibid. 13 (1978), 93-108.
[24] D. Ferus, Totally geodesic foliations, Math. Ann. 188 (1970), 313-316.
[25] S. I. Goldberg, Curvature and Homology, Academic Press, New York 1962.
[26] A. Gray, Minimal varieties and almost Hermitian submanifolds, Michigan Math. J. 12 (1965), 273-287.
[27] A. Gray, Nearly Kähler manifolds, J. Differential Geometry 4 (1970), 283-309.
[28] D. Gromoll, W. Klingenberg, W. Meyer, Riemannsche Geometrie im Grossen, Springer Verlag, 1968.
[29] A. Haefliger, Sur les classes charactéristiques des feuilletages, Séminaire Bourbaki, 1971-1972, no. 412.
[30] M. W. Hirsch, Differential Topology, Springer Verlag, 1976.
[31] H. Holmann, On the stability of holomorphic foliations with all leaves compact, Variétés Analytiques Compactes Colloque, Lecture Notes in Math. 683, Springer Verlag, 217-248.
[32] H. Holmann, Analytische periodische Strömungen auf kompakten complexen Räumen, Comment. Math. Helv. 52 (1977), 251-257.
[33] F. W. Kamber, P. Tondeur, Foliated Bundles and Characteristic Classes, Lecture Notes in Math. 493, Springer Verlag, 1975.
[34] B. Kaup, Ein geometrisches Endlichkeitskriterium für Untergruppen von Aut (C,0) und holomorphe 1-codim. Blätterungen, Comment. Math. Helv. 53 (1978), 295-299.
[35] E. Kelly, Cohomology of compact minimal submanifolds, Michigan Math. J. 19 (1972), 133-135.
[36] S. Kobayashi, K. Nomizu, Foundations of Differential Geometry, Volumes I, II, Interscience Tracts in Pure and Appl. Math., no. 15, Interscience, New York, 1963, 1969.
[37] H. B. Lawson, Rigidity theorem in rank-l symmetric spaces, J. Differential Geometry 4 (1970), 349-357.
[38] H. B. Lawson, Foliations, Bull. Amer. Math. Soc. 80 (1974), 369-418.
[39] H. B. Lawson, The quantitative theory of foliations, Amer. Math. Soc. Regional Conf. Ser. in Math. 27 (1977).
[40] Y. Matsushima, Vector bundle valued harmonic forms and immersions of Riemannian manifolds, Osaka J. Math. 8 (1971), 1-13.
[41] T. Müller, Beispiel einer periodischen instabilen holomorphen Strömung, L'Enseigment math. 25 (1980), 309-312.
[42] S. Novikov, Topology of foliations, Trudy Moskov. Mat. Obsc. 14 (1965), 248-277.
[43] J. Pasternak, Topological obstructions to integrability and Riemannian geometry of foliations, Thesis, Princeton 1970.
[44] J. F. Plante, Foliations with measure preserving holonomy, Ann. of Math. 102 (1975), 327-361.
[45] G. Reeb, Sur certaines propriétés topologiques des variétés feuilletées, Actualités Sci. Indust, no. 1183, Hermann, Paris 1952.
[46] B. L. Reinhart, The second fundamental form of a plane field, J. Differential Geometry 12 (1977), 619-628.
[47] E. A. Ruh, J. Vilms, The tension field of the Gauss map, Trans. Amer. Math. Soc. 149 (1970), 569-573.
[48] H. Rummler, Feuilletages compactes et métriques riemanniennes, I. H. E. S, preprint, 1977.
[49] H. Rummler, Une théorie de cohomologie relative pour les variétés feuilletées et son application aux feuilletages compactes, I. H. E. S, preprint, 1978.
[50] H. Rummler, Kompakte Blätterungen durch Minimalflächen, Habilitationschrift zur Erlangung der venia legendi an der math.-naturwissenschaftlichen Fakultät der Univ. Freiburg, 1979.
[51] H. Rummler, Quelques notions simples en géométrie riemannienne et leurs applications aux feuilletages compactes, Comment. Math. Helv. 54 (1979), 224-239.
[52] I. Satake, On a generalization of the notion of manifold, Proc. Nat. Acad. Sci. USA 42 (1956), 359-363.
[53] J. Simons, Minimal varieties in Riemannian manifolds, Ann. of Math. 88 (1968), 62-105.
[54] S. Sternberg, Lectures on Differential Geometry, Prentice Hall, Inc, Englewood Cliffs, N. J, 1964.
[55] D. Sullivan, A counterexample to the periodic orbit conjecture, Publ. Math, I. H. E. S, 46 (1976), 5-14.
[56] E. Vogt, Foliations of codimension 2 with all leaves compact, Manuscr. Math. 18 (1976), 187-212.
[57] A. W. Wadsley, Geodesic foliations by circles, J. Differential Geometry 10 (1975), 541-549.
[58] P. G. Walczak, A note on the volume of balls on Riemannian manifolds of non-negative curvature, to appear.
[59] P. G. Walczak, On balls and totally geodesic submanifolds, to appear in Ann. Polon. Math.
[60] J. A. Wolf, Spaces of Constant Curvature, Mc Graw-Hill, New York 1967.

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83-01-04589-2

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0012-3862

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Książka - szczegóły

On foliations with leaves satisfying some geometrical conditions

Autorzy

Seria

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