Conformal and Grassmann structures

Differential Geometry and its Application

Volumn 8, Issue 2, 1998, Pages 177-203

  Akivis, M A ^a   Goldberg, V V ^b  

^a BEN GURION UNIVERSITY OF THE NEGEV   (Israel)

^b NEW JERSEY INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Almost Grassmann structure; Conformal structure; Geometric object; Grassmann structure; Integrable almost Grassmann structure; Semiintegrable almost Grassmann structure; Structure group

Indexed keywords

EID: 0032036396     PISSN: 09262245     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0926-2245(98)00007-2     Document Type: Article

References (41)

1. [1] M.A. Akivis, Three-webs of multidimensional surfaces, Trudy Geom. Sem. Inst. Nauchn. Inform., Akad. Nauk SSSR 2 (1969) 7-31 (in Russian).
2. [2] M.A. Akivis, Webs and almost-Grassmann structures, Sibirsk. Mat. Zh. 23 (1982) (6) 6-15 (in Russian); English transl. Siberian Math. J. 23 (1982) (6) 763-770.
3. [2] M.A. Akivis, Webs and almost-Grassmann structures, Sibirsk. Mat. Zh. 23 (1982) (6) 6-15 (in Russian); English transl. Siberian Math. J. 23 (1982) (6) 763-770.
4. [3] M.A. Akivis, On the differential geometry of a Grassmann manifold, Tensor (N.S.) 38 (1982) 273-282 (in Russian).
5. [4] M.A. Akivis, Completely isotropic submanifolds of a four-dimensional pseudoconformal structure, Izv. Vyssh. Uchebn. Zaved. Mat. 1983 (1) (248) 3-11 (in Russian); English transl. Soviet Math. (Iz. VUZ) 27 (1983) (1) 1-11.
6. [4] M.A. Akivis, Completely isotropic submanifolds of a four-dimensional pseudoconformal structure, Izv. Vyssh. Uchebn. Zaved. Mat. 1983 (1) (248) 3-11 (in Russian); English transl. Soviet Math. (Iz. VUZ) 27 (1983) (1) 1-11.
7. [5] M.A. Akivis, On the theory of conformal structures, in: Geom. Sb. Vyp. 26 (Tomsk. Univ., Tomsk, 1985) 44-52 (in Russian).
8. [6] M.A. Akivis and V.V. Goldberg, Conformal Differential Geometry and Its Generalizations (Wiley-Interscience Publication, New York, 1996).
9. [7] M.A. Akivis and V.V. Konnov, Local aspects in conformal structure theory, Uspekhi Mat. Nauk 48 (1993) (1) 3-40 (in Russian); English transl. Russian Math. Surveys 48 (1993) (1) 1-35.
10. [7] M.A. Akivis and V.V. Konnov, Local aspects in conformal structure theory, Uspekhi Mat. Nauk 48 (1993) (1) 3-40 (in Russian); English transl. Russian Math. Surveys 48 (1993) (1) 1-35.
11. [8] M.A. Akivis and A.M. Shelekhov, Geometry and Algebra of Multidimensional Three-Webs (Kluwer, Dordrecht, 1992).
12. [9] M.F. Atiyah, N.L. Hitchin and I. Singer, Self-duality in four-dimensional Riemannian geometry, Proc. Roy. Soc. London Ser. A 362 (1978) 425-461.
13. [10] T.N. Bailey and M.G. Eastwood, Complex paraconformal manifolds: their differential geometry and twistor theory, Forum Math. 3 (1991) (1) 61-103.
14. [11] R.J. Baston, Almost Hermitian symmetric manifolds. I. Local twistor theory, Duke Math. J. 63 (1991) (1) 81-112.
15. [12] É. Cartan, Les sous-groupes des groupes continus de transformations, Ann. Sci. École Norm. (3) 25 (1908) 57-194; Œuvres Complètes. Partie II: Algèbre. Formes Différentielles, Systèmes Différentielles, Vols. 1-2 (Gauthier-Villars, Paris, 1953) 719-856.
16. [12] É. Cartan, Les sous-groupes des groupes continus de transformations, Ann. Sci. École Norm. (3) 25 (1908) 57-194; Œuvres Complètes. Partie II: Algèbre. Formes Différentielles, Systèmes Différentielles, Vols. 1-2 (Gauthier-Villars, Paris, 1953) 719-856.
17. [13] É. Cartan, Sur les équations de la gravitation d'Einstein, J. Math. Pures Appl. 1 (1922) 141-203; Œuvres Complètes. Partie III: Divers, Géométrie Différentielle, Vols. 1-2 (Gauthier-Villars, Paris, 1955) 549-611.
18. [13] É. Cartan, Sur les équations de la gravitation d'Einstein, J. Math. Pures Appl. 1 (1922) 141-203; Œuvres Complètes. Partie III: Divers, Géométrie Différentielle, Vols. 1-2 (Gauthier-Villars, Paris, 1955) 549-611.
19. [14] É. Cartan, Sur les espaces conformes généralisés et l'Univers optique, C.R. Acad. Sci. Paris 174 (1922) 857-859; Œuvres Complètes. Partie III: Divers, Géométrie Différentielle, Vols. 1-2 (Gauthier-Villars, Paris, 1955) 622-624.
20. [14] É. Cartan, Sur les espaces conformes généralisés et l'Univers optique, C.R. Acad. Sci. Paris 174 (1922) 857-859; Œuvres Complètes. Partie III: Divers, Géométrie Différentielle, Vols. 1-2 (Gauthier-Villars, Paris, 1955) 622-624.
21. [15] É. Cartan, Les espaces à connexion conforme, Ann. Soc. Polon. Math. 2 (1923) 171-221; Œuvres Complètes. Partie III: Divers, Géométrie Différentielle, Vols. 1-2 (Gauthier-Villars, Paris, 1955) 747-797.
22. [15] É. Cartan, Les espaces à connexion conforme, Ann. Soc. Polon. Math. 2 (1923) 171-221; Œuvres Complètes. Partie III: Divers, Géométrie Différentielle, Vols. 1-2 (Gauthier-Villars, Paris, 1955) 747-797.
23. [16] P.F. Dhooghe, Grassmannian structures on manifolds, Bull. Belg. Math. Soc. Simon Stevin 1 (1994) (1) 597-622.
24. [17] L.P. Eisenhart, Riemannian Geometry (Princeton Univ. Press, Princeton, N.J., 1926; 6th printing, 1966).
25. [18] R. Gardner, The Method of Equivalence and Its Applications (SIAM, Philadelphia, PA, 1989).
26. [19] V.V. Goldberg, (n + 1)-webs of multidimensional surfaces, Dokl. Akad. Nauk SSSR 210 (1973) (4) 756-759 (in Russian); English transl. Soviet Math. Dokl. 14 (1973) (3) 795-799.
27. [19] V.V. Goldberg, (n + 1)-webs of multidimensional surfaces, Dokl. Akad. Nauk SSSR 210 (1973) (4) 756-759 (in Russian); English transl. Soviet Math. Dokl. 14 (1973) (3) 795-799.
28. [20] V.V. Goldberg, The almost Grassmann manifold that is connected with an (n + 1)-web of multidimensional surfaces, Izv. Vyssh. Uchebn. Zaved. Mat. 1975 (8) (159) 29-38 (in Russian); English transl. Soviet Math. (Iz. VUZ) 19 (1975) (8) 23-31.
29. [20] V.V. Goldberg, The almost Grassmann manifold that is connected with an (n + 1)-web of multidimensional surfaces, Izv. Vyssh. Uchebn. Zaved. Mat. 1975 (8) (159) 29-38 (in Russian); English transl. Soviet Math. (Iz. VUZ) 19 (1975) (8) 23-31.
30. [21] V.V. Goldberg, Theory of Multidimensional (n + 1)-Webs (Kluwer, Dordrecht, 1988).
31. [22] A.B. Goncharov, Generalized conformal structures on manifolds, Selecta Math. Soviet. 6 (1987) 306-340.
32. [23] Th. Hangan, Géométrie différentielle grassmannienne, Rev. Roumaine Math. Pures Appl. 11 (1966) (5) 519-531.
33. [24] Th. Hangan, Tensor-product tangent bundles, Arch. Math. (Basel) 19 (1968) (4) 436-440.
34. [25] Th. Hangan, Sur l'intégrabilité des structures tangentes produits tensoriels réels, Ann. Mat. Pura Appl. 126 (1980) (4) 149-185.
35. [26] T. Ishihara, On tensorproduct structures and Grassmannian structures, J. Math. Tokushima Univ. 1972 (4) 1-17.
36. [27] Yu.I. Mikhailov, On the structure of almost Grassmannian manifolds, Izv. Vyssh. Uchebn. Zaved. Mat. 1978 (2) 62-72 (in Russian); English transl. Soviet Math. (Iz. VUZ) 22 (1978) (2) 54-63.
37. [27] Yu.I. Mikhailov, On the structure of almost Grassmannian manifolds, Izv. Vyssh. Uchebn. Zaved. Mat. 1978 (2) 62-72 (in Russian); English transl. Soviet Math. (Iz. VUZ) 22 (1978) (2) 54-63.
38. [28] B.A. Rosenfeld, Quasielliptic spaces, Trudy Moskov. Mat Obshch. 8 (1959) 49-70 (in Russian).
39. [29] S. Sternberg, Lectures on Differential Geometry (Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964; 2nd edition, Chelsea Publishing Co., New York, N.Y., 1983).
40. [30] H. Weyl, Reine Infinitesimalgeometrie, Math. Z. 2 (1918) 384-411.
41. [31] K. Yano, Sur les equations de Codazzi dans la géométrie conforme des espaces de Riemann, Proc. Imp. Acad. Tokyo 15 (1939) 340-344.