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)
Screen transversal lightlike submanifolds of indefinite Kaehler manifolds. (English) Zbl 1154.53308
Summary: In a spacetime, all geodesic curves fall into one of three classes; spacelike, timelike and null (lightlike) geodesic according to their tangent vectors have positive, negative or vanishing Lorentzian lengths. However, by far the most interesting curves are null curves which represent the motion of zero restmass test particles. In this paper, as a generalization of real null curves of indefinite Kaehler manifolds, we introduce screen transversal lightlike submanifolds. Then, we study the geometry of this new class (and its subspaces) and give examples.

53B30Lorentz metrics, indefinite metrics
53B25Local submanifolds
53B35Hermitian and Kählerian structures (local differential geometry)
Full Text: DOI
[1] Barros, M.; Romero, A.: Indefinite Kaehler manifolds, Math ann 261, 55-62 (1982) · Zbl 0476.53013 · doi:10.1007/BF01456410
[2] Beem, J. K.; Ehrlich, P. E.: Incompleteness of timelike submanifolds with nonvanishing second fundamental form, Gen relat gravit 17, No. 3, 293-300 (1985) · Zbl 0566.53057 · doi:10.1007/BF00760248
[3] Bejancu, A.: Geometry of CR-submanifolds, (1986) · Zbl 0605.53001
[4] Blair, D. E.; Chen, B. Y.: On CR-submanifolds of Hermitian manifolds, Israel J math 34, 353-363 (1979) · Zbl 0453.53018 · doi:10.1007/BF02760614
[5] Candelas, P.; Horowitz, G.; Strominger, A.; Witten, E.: Vacuum configurations for superstrings, Nucl phys B 258, 46-74 (1985)
[6] Claudel, C. M.; Virbhadra, K. S.; Ellis, G. F. R.: The geometry of photon surfaces, J math phys 42, 818-838 (2001) · Zbl 1061.83525 · doi:10.1063/1.1308507
[7] Duggal, K. L.; Bejancu, A.: Light-like CR-hypersurfaces of indefinite Kaehler manifolds, Acta appl math 31, 171-190 (1993) · Zbl 0782.53051 · doi:10.1007/BF00990541
[8] Duggal, K. L.; Bejancu, A.: Lightlike submanifolds of semi-Riemannian manifolds and applications, Lightlike submanifolds of semi-Riemannian manifolds and applications 364 (1996) · Zbl 0848.53001
[9] Duggal, K. L.; Sahin, B.: Screen Cauchy Riemann lightlike submanifolds, Acta math hung 106, No. 1 -- 2, 125-153 (2005)
[10] Duggal, K. L.; Sahin, B.: Generalized CR-lightlike submanifolds, Acta math hung 112, No. 1 -- 2, 107-130 (2006) · Zbl 1121.53022
[11] El Naschie, M. S.: On John Nash’s crumpled surface, Chaos, solitons & fractals 18, 635-641 (2003) · Zbl 1063.81603
[12] El Naschie, M. S.: Kähler-like manifolds, Weyl spinor particles and E-infinity high energy physics, Chaos, solitons & fractals 18, 635-641 (2003)
[13] El Naschie, M. S.: From experimental quantum optics to quantum gravity via a fuzzy Kähler manifold, Chaos, solitons & fractals 26, 665-670 (2005) · Zbl 1077.53518
[14] El Naschie, M. S.: On two new fuzzy Kähler manifolds, Chaos, solitons & fractals 29, No. 4, 876-881 (2006)
[15] Flaherty, E. J.: Hermitian and Kählerian geometry in relativity, Lecture notes in physics 46 (1976) · Zbl 0323.53048
[16] Foertsch, T.; Hasse, W.; Perlick, V.: Inertial forces and photon surfaces in arbitrary spacetimes, Classical quant grav 20, 4635-4651 (2003) · Zbl 1050.83009 · doi:10.1088/0264-9381/20/21/006
[17] Kramer, D.; Stephani, H.; Maccallum, M.; Herlt, E.: Exact solutions of Einstein’s field equations, (1980) · Zbl 0449.53018
[18] Kupeli, D. N.: Singular semi-Riemannian geometry, (1996) · Zbl 0871.53001
[19] Lerner, D. E.; Sommers, P. D.: Complex manifold techniques in theoretical physics, (1979) · Zbl 0407.00015
[20] Marek-Cmjac, C.: Fuzzy Kähler manifolds, Chaos, solitons & fractals 34, 677-681 (2007) · Zbl 1133.81061
[21] O’neill, B.: Semi-Riemannian geometry with applications to relativity, (1983)
[22] Perlick, V.: On totally umbilic submanifolds of semi-Riemannian manifolds, Nonlinear anal 63, 511-518 (2005) · Zbl 1159.53342 · doi:10.1016/j.na.2004.12.033
[23] Sahin B. Transversal lightlike submanifolds of indefinite Kaehler manifolds Analele. Universitatii din Timisoara, XLIV, 1, 2006. p. 119 -- 45. · Zbl 1174.53324
[24] Schild, A.: Classical null strings, Phys rev D 16, 1722-1726 (1977)
[25] Yano, K.; Kon, M.: CR-submanifolds of Kaehlerian and Sasakian manifolds, (1983) · Zbl 0496.53037
[26] Yau, S. T.: Calabi’s conjecture and some new results in algebraic geometry, Proc nat acad sci USA 74, 1798-1799 (1977) · Zbl 0355.32028 · doi:10.1073/pnas.74.5.1798