Calvaruso, G.:
Three-Dimensional Paracontact Walker Structures
Bollettino dell'Unione Matematica Italiana Serie 9 5 (2012), fasc. n.2, p. 387-403, (English)
pdf (310 Kb), djvu (163 Kb). | MR 2977255 | Zbl 1264.53036
Sunto
We investigate paracontact metric three-manifolds equipped with an associated Walker metric. Some interesting paracontact metric properties are studied for the paracontact Walker structures introduced in [10], also clarifying their relationships with some curvature properties. Moreover, improving the result on [4] on locally symmetric Walker three-manifolds, we show that homogeneity conditions give some obstructions to the existence of compatible paracontact structures on a Walker three-manifold.
Referenze Bibliografiche
[1]
D. E. BLAIR -
T. KOUFOGIORGOS -
R. SHARMA,
A classification of 3-dimensional contact metric manifolds with $Q\phi = \phi Q$,
Kodai Math. J. 13 (
1990), 391-401. |
fulltext (doi) |
MR 1078554[2]
G. CALVARUSO,
Homogeneous structures on three-dimensional Lorentzian manifolds,
J. Geom. Phys.,
57 (
2007), 1279-1291.
Addendum:
J. Geom. Phys.,
58 (
2008), 291-292. |
fulltext (doi) |
MR 2384316 |
Zbl 1112.53051[4]
G. CALVARUSO,
Homogeneous paracontact metric three-manifolds,
Illinois J. Math., to appear. |
MR 3020703 |
Zbl 1273.53020[5]
G. CALVARUSO -
B. DE LEO,
Semi-symmetric Lorentzian three-manifolds admitting a parallel degenerate line field,
Mediterr. J. Math.,
7 (
2010), 89-100. |
fulltext (doi) |
MR 2645904 |
Zbl 1193.53146[8]
M. CHAICHI -
E. GARCÍA-RÍO -
M. E. VÁZQUEZ-ABAL,
Three-dimensional Lorentz manifolds admitting a parallel null vector field,
J. Phys. A: Math. Gen.,
38 (
2005), 841-850. |
fulltext (doi) |
MR 2125237 |
Zbl 1068.53049[9]
L. A. CORDERO -
P. E. PARKER,
Left-invariant Lorentzian metrics on 3-dimensional Lie groups,
Rend. Mat. Serie VII,
17 (
1997), 129-155. |
MR 1459412 |
Zbl 0948.53027[10]
E. GARCÍA-RÍO -
A. HAJI-BADALI -
M. E. VÁZQUEZ-ABAL -
R. VÁZQUEZ-LORENZO,
On the local geometry of three-dimensional Walker metrics,
Advances in Lorentzian Geometry 77-87,
Shaker Verlag, Aachen,
2008. |
MR 2603188 |
Zbl 1161.53353[11]
S. KANEYUKI -
M. KONZAI,
Paracomplex structures and affine symmetric spaces,
Tokyo J. Math.,
8 (
1985), 301-318. |
fulltext (doi) |
MR 800077[13]
P. LIBERMANN,
Sur les structures presque paracomplexes,
C. R. Acad. Sci. Paris,
234 (
1952), 2517-2519. |
MR 48893 |
Zbl 0046.15601[14]
B. O'NEILL,
Semi-Riemannian Geometry, New York:
Academic Press,
1983. |
MR 719023[16]
A. G. WALKER,
Canonical form for a Riemannian space with a parallel field of null planes,
Quart. J. Math. Oxford,
1 (
1950), 69-79. |
fulltext (doi) |
MR 35085 |
Zbl 0036.38303