Some properties of closed -forms on a special Riemannian manifold

Author:
Gr. Tsagas

Journal:
Proc. Amer. Math. Soc. **81** (1981), 104-106

MSC:
Primary 53C20

DOI:
https://doi.org/10.1090/S0002-9939-1981-0589147-5

MathSciNet review:
589147

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a compact Riemannian manifold whose sectional curvature is strictly negative; then every closed -form on has a singularity.

**[1]**R. L. Bishop and B. O'Neil,*Manifolds of negative curvature*, Trans. Amer. Math. Soc.**145**(1969), 1-49. MR**0251664 (40:4891)****[2]**W. Byers,*On a theorem of Preissmann*, Proc. Amer. Math. Soc.**24**(1970), 50-51. MR**0251665 (40:4892)****[3]**F. T. Farrell,*The obstruction to fibering a manifold over a circle*, Indiana Univ. Math. J.**21**(1971), 315-346. MR**0290397 (44:7578)****[4]**D. Gromol and J. Wolf,*Some relations between the metric structure and the algebraic structure of the fundamental group in the manifolds of nonpositive curvature*, Bull. Amer. Math. Soc.**77**(1971), 545-552. MR**0281122 (43:6841)****[5]**S. T. Hu,*Homotopy theory*, Academic Press, New York, 1963. MR**0106454 (21:5186)****[6]**J. Milnor,*Lectures on Morse theory*, Ann. of Math. Studies, No. 51, Princeton Univ. Press, Princeton, N.J., 1963. MR**0163331 (29:634)****[7]**-,*A note on curvature and fundamental group*, J. Differential Geometry**2**(1968), 1-7. MR**0232311 (38:636)****[8]**-,*Growth of finitely generated solvable groups*, J. Differential Geometry**2**(1968), 427-449. MR**0244899 (39:6212)****[9]**Gr. Tsagas,*On the singularities of harmonic**-forms on a Riemannian manifold*, Kōdai Math. Sem. Rep.**26**(1975), 459-466. MR**0394506 (52:15307)****[10]**D. Tischler,*On fibering certain foliated manifolds over*, Topology**9**(1970), 153-154. MR**0256413 (41:1069)****[11]**J. A. Wolf,*Growth of finitely generated solvable groups and curvature of Riemannian manifolds*, J. Differential Geometry**2**(1970), 421-446. MR**0248688 (40:1939)****[12]**S. Yau,*On the fundamental group of compact manifolds of non-positive curvature*, J. Differential Geometry**6**(1971), 579-585. MR**0283726 (44:956)**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
53C20

Retrieve articles in all journals with MSC: 53C20

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1981-0589147-5

Keywords:
Riemannian manifold,
closed -form,
harmonic -form,
negative -pinched,
singularity of -forms.

Article copyright:
© Copyright 1981
American Mathematical Society