A Weitzenbôck formula for the second fundamental form of a Riemannian foliation

Paolo Piccinni

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1984)

  • Volume: 77, Issue: 3-4, page 102-110
  • ISSN: 1120-6330

How to cite

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Piccinni, Paolo. "A Weitzenbôck formula for the second fundamental form of a Riemannian foliation." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 77.3-4 (1984): 102-110. <http://eudml.org/doc/287301>.

@article{Piccinni1984,
author = {Piccinni, Paolo},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {flat normal connection; Riemannian foliation; Weitzenböck formula; constant sectional curvature; second fundamental form; Riemannian submersions; mean curvature; totally geodesic},
language = {eng},
month = {9},
number = {3-4},
pages = {102-110},
publisher = {Accademia Nazionale dei Lincei},
title = {A Weitzenbôck formula for the second fundamental form of a Riemannian foliation},
url = {http://eudml.org/doc/287301},
volume = {77},
year = {1984},
}

TY - JOUR
AU - Piccinni, Paolo
TI - A Weitzenbôck formula for the second fundamental form of a Riemannian foliation
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1984/9//
PB - Accademia Nazionale dei Lincei
VL - 77
IS - 3-4
SP - 102
EP - 110
LA - eng
KW - flat normal connection; Riemannian foliation; Weitzenböck formula; constant sectional curvature; second fundamental form; Riemannian submersions; mean curvature; totally geodesic
UR - http://eudml.org/doc/287301
ER -

References

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  1. CHEN, B.Y. (1984) - Total mean curvature and submanifolds of finite type, «World Scientific Series on Pure Math.». Zbl0537.53049MR749575DOI10.1142/0065
  2. KAMBER, F.W. and TONDEUR, PH. (1982) - Harmonic foliations, Proc. of the NSF Conference on Harmonic MapsTulane University 1980, «Springer Lect. Notes», 949, 87-121. Zbl0511.57020MR673585
  3. KAMBER, F.W. and TONDEUR, PH. - Curvature properties of harmonic foliations, «Illinois J. of Math.», to appear. Zbl0529.53027MR748954
  4. O'NEILL, B. (1966) - The fundamental equation of a submersion. «Michigan Math. J.», 13, 459-469. Zbl0145.18602MR200865
  5. O'NEILL, B. (1983) - Semi-Riemannian geometry, Academic Press. MR719023
  6. REINHART, B.L. (1983) - Differential Geometry of Foliations, Springer. Zbl0506.53018MR705126DOI10.1007/978-3-642-69015-0
  7. SIMONS, J. (1968) - Minimal varieties in Riemannian manifolds, «Ann. of Math.», 88, 62-105. Zbl0181.49702MR233295
  8. WU, H. (1982) - The Bochner technique, Proc. of the 1980 Beijing Symposium on Diff. Geometry and Diff. Equations, Science Press, China, 2, 929-1071. Zbl0528.53042MR714349
  9. YANO, K. and KON, M. (1983) - CR-submanifolds of Kaehlerian and Sasakian manifolds, Birkhäusen. Zbl0496.53037MR688816

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