zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Generalized Sasakian-space-forms. (English) Zbl 1064.53026
The authors introduce generalized Sasakian-space-forms and study their basic properties. They state that every generalized Sasakian-space-form with a K-contact structure is a Sasakian manifold, and, if the dimension is 5, a Sasakian-space-form. The conditions for a generalized Sasakian-space-form to be a contact metric manifold are investigated. To construct many examples of these manifolds the authors use a wide variety of geometric constructions, such as Riemannian submersions, product manifolds, warped products, conformal transformations, D-homothetic deformations and D-conformal deformations. Some further results on generalized complex-space-forms are also stated.

53C25Special Riemannian manifolds (Einstein, Sasakian, etc.)
[1]D. E. Blair,The theory of quasi-Sasakian structures, Journal of Differential Geometry1 (1967), 331–345.
[2]D. E. Blair,Riemannian Geometry of Contact and Symplectic Manifolds, Birkhäuser, Boston, 2002.
[3]P. Bueken and L. Vanhecke,Curvature characterizations in contact geometry, Rivista di Matematica della Università di Parma (4)14 (1988), 303–313.
[4]B. Y. Chen,Total Mean Curvature and Submanifolds of Finite Type, Series in Pure Mathematics 1, World Scientific, Singapore, 1984.
[5]S. Ianus and D. Smaranda,Some remarkable structures on the product of an almost contact metric manifold with the real line, inNational Colloquium on Geometry and Topology, University of Timişoara, 1977, pp. 107–110.
[6]D. Janssens and L. Vanhecke,Almost contact structures and curvature tensors, Kodai Mathematical Journal4 (1981), 1–27. · Zbl 0472.53043 · doi:10.2996/kmj/1138036310
[7]K. Kenmotsu,A class of almost contact Riemannian manifolds, Tôhoku Mathematical Journal24 (1972), 93–103. · Zbl 0245.53040 · doi:10.2748/tmj/1178241594
[8]G. D. Ludden,Submanifolds of cosymplectic manifolds, Journal of Differential Geometry4 (1970), 237–244.
[9]J. C. Marrero,The local structure of trans-Sasakian manifolds, Annali di Matematica Pura ed Applicata162 (1992), 77–86. · Zbl 0772.53036 · doi:10.1007/BF01760000
[10]Z. Olszak,On the existence of generalized complex space forms, Israel Journal of Mathematics65 (1989), 214–218. · Zbl 0674.53061 · doi:10.1007/BF02764861
[11]B. O’Neill,Semi-Rimannian Geometry with Applications to Relativity, Pure and Applied Mathematics 103, Academic Press, New York, 1983.
[12]J. A. Oubiña,New classes of almost contact metric structures, Publications Mathematicae Debrecen32 (1985), 187–193.
[13]R. Sharma,On the curvature of contact metric manifolds, Journal of Geometry53 (1995), 179–190. · Zbl 0833.53033 · doi:10.1007/BF01224050
[14]S. Suguri and S. Nakayama,D-conformal deformations on almost contact metric structure, Tensor. New Series28 (1974), 125–129.
[15]S. Tanno,The topology of contact Riemannian manifolds, Illinois Journal of Mathematics12 (1968), 700–717.
[16]F. Tricerri and L. Vanhecke,Curvature tensors on almost Hermitian manifolds, Transactions of the American Mathematical Society267 (1981), 365–398. · doi:10.1090/S0002-9947-1981-0626479-0
[17]I. Vaisman,Conformal changes of almost contact metric structures, inGeometry and Differential Geometry, Lecture Notes in Mathematics792, Springer-Verlag, Berlin, 1980, pp. 435–443.
[18]L. Vanhecke,Almost Hermitian manifolds with J-invariant Riemann curvature tensor, Rendiconti del Seminario Mathematico della Universitá e Politecnico di Torino34 (1975–76), 487–498.