We shall survey our work on Riemannian geometry of tangent sphere bundles with arbitrary constant radius done since the year 2000.
@article{127125, author = {Old\v rich Kowalski and Masami Sekizawa}, title = {On Riemannian geometry of tangent sphere bundles with arbitrary constant radius}, journal = {Archivum Mathematicum}, volume = {044}, year = {2008}, pages = {391-401}, zbl = {1212.53043}, mrnumber = {2501575}, language = {en}, url = {http://dml.mathdoc.fr/item/127125} }
Kowalski, Oldřich; Sekizawa, Masami. On Riemannian geometry of tangent sphere bundles with arbitrary constant radius. Archivum Mathematicum, Tome 044 (2008) pp. 391-401. http://gdmltest.u-ga.fr/item/127125/
$g$-natural contact metrics on unit tangent sphere bundles, Monatsh. Math. 151 (2) (2007), 89–109. (2007) | Article | MR 2322938 | Zbl 1128.53049
On the non-existence of elements of Hopf invariant one, Ann. Math. 72 (1960), 20–104. (1960) | Article | MR 0141119 | Zbl 0096.17404
Einstein Manifolds, Springer-Verlag, Berlin–Heidelberg–New York, 1987. (1987) | MR 0867684 | Zbl 0613.53001
When is the tangent sphere bundle locally symmetric?, Geom. Topol., World Sci. Publishing, Singapore (1989), 15–30. (1989) | MR 1001586
Characteristic reflections on unit tangent sphere bundles, Houston J. Math. 23 (1997), 427–448. (1997) | MR 1690045 | Zbl 0897.53010
Geometry of the tangent sphere bundle, Proceedings of the Workshop on Recent Topics in Differential Geometry (Cordero, L. A., García-Río, E., eds.), Santiago de Compostela, 1997, pp. 5–17. (1997)
Curvature homogeneous unit tangent sphere bundles, Publ. Math. Debrecen 35 (1998), 389–413. (1998) | MR 1657491
Unit tangent sphere bundles and two-point homogeneous spaces, Period. Math. Hungar. 36 (1998), 79–95. (1998) | Article | MR 1694613
Harmonic and minimal vector fields on tangent and unit tangent bundles, Differential Geom. Appl. 13 (2000), 77–93. (2000) | Article | MR 1775222 | Zbl 0973.53053
Unit tangent sphere bundles with constant scalar curvature, Czechoslovak Math. J. 51 (126) (2001), 523–544. (2001) | Article | MR 1851545 | Zbl 1079.53063
On the Sasaki metric of the tangent and the normal bundles, Sov. Math., Dokl. 35 (1987), 479–482. (1987)
The sectional curvature of the Sasaki metric of $T_rM^n$, Ukrain. Geom. Sb. 30 (1987), 10–17. (1987)
Riemannian geometry of fiber bundles, Russian Math. Surveys 46 (6) (1991), 55–106. (1991) | Article | MR 1164201
Contact metric geometry of the unit tangent sphere bundle, Complex, contact and symmetric manifolds. In honor of L. Vanhecke (Kowalski, O. et al, ed.), vol. 234, Progress in Mathematics, 2005, pp. 41–57. (2005) | MR 2105140 | Zbl 1079.53045
Riemannian manifold in which the skew-symmetric curvature operator has pointwise constant eigenvalues, Geom. Dedicata 70 (1998), 269–282. (1998) | Article | MR 1624814 | Zbl 0903.53016
Foundations of Differential Geometry II, Interscience Publishers, New York–London–Sydney, 1969. (1969) | MR 0238225
Geometry of tangent sphere bundles with arbitrary constant radius, Proceedings of the Symposium Contemporary Mathematics (Bokan, N., ed.), Faculty of Mathematics, University of Belgrade, 2000, pp. 219–228. (2000) | MR 1848571 | Zbl 1024.53030
On tangent sphere bundles with small or large constant radius, Ann. Global Anal. Geom. 18 (2000), 207–219. (2000) | Article | MR 1795094 | Zbl 1011.53025
On the scalar curvature of tangent sphere bundles with arbitrary constant radius, Bull. Greek Math. Soc. 44 (2000), 17–30. (2000) | MR 1848571 | Zbl 1163.53321
On Riemannian manifolds whose tangent sphere bundles can have nonnegative sectional curvature, Univ. Jagellon. Acta Math. 40 (2002), 245–256. (2002) | MR 1962729 | Zbl 1039.53050
Can tangent sphere bundles over Riemannian manifolds have strictly positive sectional curvature?, Global Differential Geometry: The Mathematical Legacy of Alfred Gray (Fernandez, M. and Wolf, J. A., eds.), Contemp. Math. 288 (2001), 110–118. (2001) | Article | MR 1871003 | Zbl 1011.53034
Geodesics on the tangent sphere bundle of a Riemannian manifold, Geom. Dedicata 7 (1978), 233–243. (1978) | MR 0487892 | Zbl 0385.53010
Positive Ricci curvature on fiber bundles, J. Differential Geom. 14 (1979), 241–254. (1979) | MR 0587552
Isometries of tangent sphere bundles, Boll. Un. Mat. Ital. A(7) 5 (1991), 207–214. (1991) | MR 1120381
Some exotic spheres with positive Ricci curvature, Math. Ann. 216 (1975), 245–252. (1975) | Article | MR 0400110 | Zbl 0293.53016
Conformally flat Riemannian manifolds admitting a transitive group of isometries, Tôhoku Math. J. 27 (1975), 103–110. (1975) | Article | MR 0442852 | Zbl 0323.53037
Elliptic spaces in Grassmann manifolds, Illinois J. Math. 7 (1963), 447–462. (1963) | MR 0156295
On the geometry of tangent sphere bundles of Riemannian manifolds, Ukrain. Geom. Sb 24 (1981), 129–132, in Russian. (1981) | MR 0629822
On Sasaki metric of tangent and normal bundle, Ph.D. thesis, Odessa, 1986, (Russian). (1986)