This is a preview of subscription content, log in via an institution to check access.
References
D. E. Blair, Contact Manifolds in Riemannian Geometry, Lecture Notes in Mathematics 509, Springer-Verlag (Berlin-Heidelberg-New York, 1976).
D. E. Blair and B. J. Papantonion, A characterization of Sasakian space forms by geodesic tubes, Math. J. Toyama Univ., 16 (1993), 65-90.
D. E. Blair and L. Vanhecke, Geodesic spheres and Jacobi vector fields in Sasakian space forms, Proc. Roy. Soc. Edinburgh, A105 (1987), 17-22.
D. E. Blair and L. Vanhecke, Symmetries and φ-symmetric spaces, Tôhoku Math. J., 39 (1987), 373-383.
D. E. Blair and L. Vanhecke, New characterizations of φ-symmetric spaces, Kodai Math. J., 10 (1987), 102-107.
P. Bueken, Reflections and rotations in contact geometry, doctoral dissertation, Katholieke Universiteit Leuven, 1992.
P. Bueken and L. Vanhecke, Geometry and symmetry on Sasakian manifolds, Tsukuba Math. J., 12 (1988), 403-422.
B. Y. Chen and L. Vanhecke, Differential geometry of geodesic spheres, J. Reine Angew. Math., 325 (1981), 28-67.
M. Djorić and L. Vanhecke, Almost Hermitian geometry, geodesic spheres and symmetries, Math. Okayama Univ., 32 (1990), 187-206.
M. Djorić and L. Vanhecke, Geometry of geodesic spheres on Sasakian manifolds, Rend. Sem. Mat. Univ. Pol. Torino, 49 (1991), 329-357.
M. Djorić and L. Vanhecke, Geometry of tubes about characteristic curves on Sasakian manifolds, Rend. Circ. Mat. Palermo, XLI (1992), 111-122.
M. Djorić, On characterizations of Sasakian space forms and locally φ-symmetric spaces by φ-geodesic tubes, Publ. Math. Debrecen, 46 (1995), 1-23.
L. Gheysens and L. Vanhecke, Total scalar curvature of tubes about curves, Math. Nachr., 103 (1981), 177-197.
A. Gray and L. Vanhecke, Riemannian geometry as determined by the volumes of small geodesic balls, Acta Math., 142 (1979), 157-198.
A. Gray and L. Vanhecke, The volume of tubes about curves in a Riemannian manifold, Proc. London Math. Soc., 44 (1982), 215-243.
A. Gray, Tubes, Addison-Wesley Publ. Co. (Reading, 1990).
S. Kobayashi and K. Nomizn, Foundations of Differential geometry, I–II (1963), J. Wiley.
K. Ogiue, On fiberings of almost contact manifolds, Kōdai Math. Sem. Rep., 17 (1965), 53-62.
M. Okumura, Some remarks on spaces with a certain contact structure, Tôhoku Math. J., 14 (1962), 135-145.
S. Sekigawa and L. Vanhecke, Symplectic geodesic symmetries on Kähler manifolds, Quart. J. Math. Oxford, 37 (1986), 95-103.
T. Takahashi, Sasakian φ-symmetric spaces, Tôhoku Math. J., 29 (1977), 91-113.
S. Tanno, Constancy of holomorphic sectional curvature in almost Hermitian manifolds, Kōdai Math. Sem. Rep., 25 (1973), 190-201.
L. Vanhecke, Geometry in normal and tubular neighborhoods, Rend. Sem. Fac. Sci. Univ. Cagliari, Supplemento al Vol. 58 (1988), 73-176.
K. Yano and M. Kon, Structures on Manifolds, Series in Pure Mathematics, 3, World Scientific Publ. Co. (Singapore, 1984).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Djorić, M. Geometry of Tubes About ϕ-Geodesics on Sasakian Manifolds. Acta Mathematica Hungarica 75, 137–159 (1997). https://doi.org/10.1023/A:1006538903081
Issue Date:
DOI: https://doi.org/10.1023/A:1006538903081