Uneingeschränkter Zugang

Riemannian foliations and the kernel of the basic Dirac operator

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică's Cover Image
Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică
Proceedings of the 10th International Workshop on Differential Geometry and its Applications

Zitieren

[1] J. A. Alvarez Lopez, The basic component of the mean curvature of Riemannian foliations, Ann. Global Anal. Geom. 10 (1992), 179-194.10.1007/BF00130919Search in Google Scholar

[2] J. A. Alvarez Lopez, Y.A. Kordyukov, Adiabatic limits and spectral sequences for Riemannian foliations, Geom. and Funct. Anal. 10 (2000), 977-1027.10.1007/PL00001653Search in Google Scholar

[3] J. Brüning, F.W. Kamber, Vanishing theorems and index formulas for transversal Dirac operators, AMS Meeting 845, Special Session on Op- erator Theory and Applications to Geometry, American Mathematical Society Abstracts, Lawrence, KA, 1988.Search in Google Scholar

[4] M. Craioveanu, M. Puta, Asymptotic properties of eigenvalues of the basic Laplacian associated to certain Riemannian foliations, Bull. Math. Soc. Sei. Math. Roumanie, (NS) 35 (1991), C1-C5.Search in Google Scholar

[5] D. Dominguez, A tenseness theorem for Riemannian foliations, C. R. Acad. Sci. Sér. I 320 (1995), 1331-1335.Search in Google Scholar

[6] J. F. Glazebrook, F. W. Kamber, Transversal Dirac families in Riemannian foliations. Commun. Math. Phys. 140(1991), 217-240.Search in Google Scholar

[7] M. Gromov, H. B. Lawson, Spin and scalar curvature in the presence of a fundamental group I, Ann. of Math. 111(1980), 209-230.10.2307/1971198Search in Google Scholar

[8] G. Habib, Tenseur dimpulsion-énergie et feuilletages, Ph.D thesis (2000), Université Henri Poincaré, Nancy.Search in Google Scholar

[9] G. Habib, K. Richardson, A brief note on the spectrum of the basic Dirac operator, Bull. London Math. Soc. 41 (2009), 083-090.10.1112/blms/bdp042Search in Google Scholar

[10] O. Hijazi, A conformai lower bound for the smallest eigenvalue of the Dirac operator and Killing spinors, Commun. Math. Phys. 104 (1980), 151-102.10.1007/BF01210797Search in Google Scholar

[11] S. D. Jung, The first eigenvalue of the transversal Dirac operator. J. Geom. Phys. 39 (2001), 253-204.Search in Google Scholar

[12] F. Kamber, Ph. Tondeur, De Rham-Hodge theory for Riemannian folia- tions, Math. Ann. 277 (1987), 425-431.10.1007/BF01458323Search in Google Scholar

[13] A. El Kacimi Alaoui, M. Nicolau, On the topological invariance of the basic cohomology, Math. Ann. 295 (1993), 027-034.Search in Google Scholar

[14] Y. A. Kordyukov, Vanishing theorem for transverse Dirac operators on Riemannian foliations, Ann. Glob. Anal. Geom. 34 (2008), 195-211.10.1007/s10455-008-9103-2Search in Google Scholar

[15] H. B. Lawson, M. L. Michelsohn, Spin geometry, Princeton University Press, 1989.Search in Google Scholar

[16] A. Mason, An application of stochastic flows to Riemannian foliations, Houston J. Math. 20 (2000), 481-515.Search in Google Scholar

[17] E. Park, K. Richardson, The basic Laplacian of a Riemannian foliation, Amer. J. Math. 118 (1990), 1249-1275.10.1353/ajm.1996.0053Search in Google Scholar

[18] B. Reinhart, Foliated manifolds with bundle-like metrics. Ann. Math. 09 (1959), 119-132. Search in Google Scholar

[19] V. Slesar, Weitzenböck formulas for Riemannian foliations, Diff. Geom. App. 27 (2009), 362-367.10.1016/j.difgeo.2008.10.014Search in Google Scholar

[20] V. Slesar, On the Dirac spectrum of Riemannian foliations admitting a basic parallel 1- form, J. Geom. Phys. 62 (2012), 804-813.10.1016/j.geomphys.2012.01.004Search in Google Scholar

[21] Ph. Tondeur, Geometry of Foliations, Birkhäuser, Basel, Boston, 1997.10.1007/978-3-0348-8914-8Search in Google Scholar

eISSN:
1844-0835
Sprache:
Englisch
Zeitrahmen der Veröffentlichung:
Volume Open
Fachgebiete der Zeitschrift:
Mathematik, Allgemeines