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Tangent sphere bundles satisfying ∇ξτ=0

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References

  1. BLAIR D.E.:Contact Manifolds in Riemannian Geometry, Lect. Notes Math. 509, Berlin, Springer, 1976.

    Google Scholar 

  2. BLAIR D.E.:When is the tangent sphere bundle locally symmetric?, Geometry and Topology, World Scientific, Singapore, 1989, 15–30.

    Google Scholar 

  3. CARPENTER P., GRAY A., WILLMORE T. J.:The curvature of Einstein symmetric spaces, Quart. J. Math. Oxford (2),33 (1982), 45–64.

    Google Scholar 

  4. CARTAN E.:Geometry of Riemannian Spaces, Math. Sci. Press, Brookline Mass., 1983.

    Google Scholar 

  5. CHEN B.Y., VANHECKE L.:Differential geometry of geodesic spheres, J. Reine Angew Math.325 (1981), 28–67.

    Google Scholar 

  6. CHERN S.S., HAMILTON R.S.:On Riemannian metrics adapted to three-dimensional contact manifolds, Lect. Notes Math. 1111. Berlin, Springer, 1985, pp.279–308.

    Google Scholar 

  7. KOWALSKI O.:Curvature of the induced Riemannian metric on the tangent bundle of a Riemannian manifold, J. Reine Angew. Math.250, 124–129 (1971).

    Google Scholar 

  8. MUSSO E., TRICERRI F.:Riemannian metrics on tangent bundles, Annali di MatematicaCL, 1–19 (1988).

    Google Scholar 

  9. PERRONE D.:Torsion and critical metrics on contact three-manifolds, Kodai Math. J.13, 88–100 (1990).

    Google Scholar 

  10. PERRONE D.:Torsion tensor and critical metrics on contact (2n+1)- maifolds, Mh. Math.114, 245–259 (1992).

    Google Scholar 

  11. PERRONE D.:Contact Riemannian manifolds satisfying R(X,ξ)·R=0, Yokohama Math. J.39, 141–149 (1992).

    Google Scholar 

  12. TANNO S.:Locally symmetric K-contact Riemannian manifolds, Proc. Japan Acad.43, 581–583 (1967).

    Google Scholar 

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Dedicated to professor N.K. Stephanidis on his 65th birthday

Supported by funds of the M.R.S.T.

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Perrone, D. Tangent sphere bundles satisfying ∇ξτ=0. J Geom 49, 178–188 (1994). https://doi.org/10.1007/BF01228060

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  • DOI: https://doi.org/10.1007/BF01228060

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