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Volumn 110, Issue 1, 2010, Pages 73-107

Curve flows and solitonic hierarchies generated by Einstein metrics

Author keywords

(Semi) Riemannian spaces; Bi Hamiltonian; Curve flow; Nonholonomic manifold; Nonlinear connection; Solitonic equations

Indexed keywords

(SEMI) RIEMANNIAN SPACES; CONTINUOUS MEDIA; EXPLICIT FORM; FUNDAMENTAL THEORY; GEOMETRIC CONSTRUCTION; GEOMETRIC MECHANICS; GRAVITATIONAL INTERACTION; HAMILTONIAN STRUCTURES; LINEAR CONNECTIONS; NONHOLONOMICS; NONLINEAR CONNECTIONS; NONLINEAR WAVES; RIEMANNIAN METRICS; RIEMANNIAN SPACES; SINE-GORDON EQUATION; SPACETIME;

EID: 77952054500     PISSN: 01678019     EISSN: 15729036     Source Type: Journal    
DOI: 10.1007/s10440-008-9387-z     Document Type: Article
Times cited : (23)

References (34)
  • 1
    • 17644398195 scopus 로고    scopus 로고
    • Exact solutions with noncommutative symmetries in Einstein and gauge gravity
    • DOI 10.1063/1.1869538, 042503
    • S. Vacaru 2005 Exact solutions with noncommutative symmetries in Einstein and gauge gravity J. Math. Phys. 46 042503 10.1063/1.1869538 2131241 (Pubitemid 40560091)
    • (2005) Journal of Mathematical Physics , vol.46 , Issue.4 , pp. 1-47
    • Vacaru, S.I.1
  • 2
    • 38049046236 scopus 로고    scopus 로고
    • Parametric nonholonomic frame transforms and exact solutions in gravity
    • 1158.83010 10.1142/S0219887807002570 2378384
    • S. Vacaru 2007 Parametric nonholonomic frame transforms and exact solutions in gravity Int. J. Geom. Methods Mod. Phys. [IJGMMP] 4 1285 1334 1158.83010 10.1142/S0219887807002570 2378384
    • (2007) Int. J. Geom. Methods Mod. Phys. [IJGMMP] , vol.4 , pp. 1285-1334
    • Vacaru, S.1
  • 3
    • 43049123148 scopus 로고    scopus 로고
    • Nonholonomic Ricci flows: II. Evolution equations and dynamics
    • 10.1063/1.2899316 2412299
    • S. Vacaru 2008 Nonholonomic Ricci flows: II. Evolution equations and dynamics J. Math. Phys. 49 043504 10.1063/1.2899316 2412299
    • (2008) J. Math. Phys. , vol.49 , pp. 043504
    • Vacaru, S.1
  • 5
    • 60449110303 scopus 로고    scopus 로고
    • Nonholonomic Ricci flows, exact solutions in gravity, and symmetric and nonsymmetric metrics
    • doi: 10.1007/s10773-008-9841-8, arXiv:0806.3812[gr-qc]
    • Vacaru, S.: Nonholonomic Ricci flows, exact solutions in gravity, and symmetric and nonsymmetric metrics. Int. J. Theor. Phys. 47 (2008). doi: 10.1007/s10773-008-9841-8. arXiv:0806.3812 [gr-qc]
    • (2008) Int. J. Theor. Phys. , vol.47
    • Vacaru, S.1
  • 7
    • 47149112241 scopus 로고    scopus 로고
    • Finsler and Lagrange geometries in Einstein and string gravity
    • 1152.53016 10.1142/S0219887808002898 2428807
    • S. Vacaru 2008 Finsler and Lagrange geometries in Einstein and string gravity Int. J. Geom. Methods. Mod. Phys. [IJGMMP] 5 473 511 1152.53016 10.1142/S0219887808002898 2428807
    • (2008) Int. J. Geom. Methods. Mod. Phys. [IJGMMP] , vol.5 , pp. 473-511
    • Vacaru, S.1
  • 10
    • 0036467962 scopus 로고    scopus 로고
    • Integrable equations arising from motions of plane curves
    • DOI 10.1016/S0167-2789(01)00364-5, PII S0167278901003645
    • K.-S. Chou C. Qu 2002 Integrable equations arising from motions of plane curves Phys. D 162 9 33 0987.35139 10.1016/S0167-2789(01)00364-5 1882237 (Pubitemid 34105485)
    • (2002) Physica D: Nonlinear Phenomena , vol.162 , Issue.1-2 , pp. 9-33
    • Chou, K.-S.1    Qu, C.2
  • 11
    • 0013097341 scopus 로고    scopus 로고
    • Integrable systems in three-dimensional Riemannian geometry
    • DOI 10.1007/s00332-001-0472-y
    • G. Mari Beffa J. Sanders J.-P. Wang 2002 Integrable systems in three-dimensional Riemannian geometry J. Nonlinear. Sci. 12 143 167 1140.37361 10.1007/s00332-001-0472-y 1894465 (Pubitemid 135696006)
    • (2002) Journal of Nonlinear Science , vol.12 , Issue.2 , pp. 143-167
    • Mari Beffa, G.1    Sanders, J.A.2    Wang, J.P.3
  • 12
    • 36149028354 scopus 로고
    • Local Hamiltonian structures of multicomponent KdV equations
    • 0692.35101 10.1088/0305-4470/21/24/010 974701
    • C. Athorne 1988 Local Hamiltonian structures of multicomponent KdV equations J. Phys. A: Math. Gen. 21 4549 4556 0692.35101 10.1088/0305-4470/21/ 24/010 974701
    • (1988) J. Phys. A: Math. Gen. , vol.21 , pp. 4549-4556
    • Athorne, C.1
  • 13
    • 29544443226 scopus 로고    scopus 로고
    • Integrable systems in n dimensional Riemannian geometry
    • 1050.37035 2058803
    • J. Sanders J.-P. Wang 2003 Integrable systems in n dimensional Riemannian geometry Mosc. Math. J. 3 1369 1393 1050.37035 2058803
    • (2003) Mosc. Math. J. , vol.3 , pp. 1369-1393
    • Sanders, J.1    Wang, J.-P.2
  • 14
    • 24144500759 scopus 로고    scopus 로고
    • Why nonlocal recursion operators produce local symmetries: New results and applications
    • DOI 10.1088/0305-4470/38/15/011
    • A. Sergyeyev 2005 Why nonlocal recursion operators produce local symmetries: new results and applications J. Phys. A: Math. Gen. 38 3397 3407 1065.37051 10.1088/0305-4470/38/15/011 2132718 (Pubitemid 41236953)
    • (2005) Journal of Physics A: Mathematical and General , vol.38 , Issue.15 , pp. 3397-3407
    • Sergyeyev, A.1
  • 15
    • 0034345883 scopus 로고    scopus 로고
    • Classification of certain integrable coupled potential KdV and modified KdV-type equations
    • 0987.37064 10.1063/1.1287643 1779638
    • M.V. Foursov 2000 Classification of certain integrable coupled potential KdV and modified KdV-type equations J. Math. Phys. 41 6173 6185 0987.37064 10.1063/1.1287643 1779638
    • (2000) J. Math. Phys. , vol.41 , pp. 6173-6185
    • Foursov, M.V.1
  • 16
    • 2042467083 scopus 로고    scopus 로고
    • Generalized Hasimoto transformation and vector sine-Gordon equation
    • S. Abenda G. Gaeta S. Walcher (eds). World Scientific River Edge
    • Wang, J.-P.: Generalized Hasimoto transformation and vector sine-Gordon equation. In: Abenda, S., Gaeta, G., Walcher, S. (eds.) SPT 2002: Symmetry and Perturbation Theory (Cala Gonone), pp. 276-283. World Scientific, River Edge (2002)
    • (2002) SPT 2002: Symmetry and Perturbation Theory (Cala Gonone) , pp. 276-283
    • Wang, J.-P.1
  • 17
    • 84889235405 scopus 로고    scopus 로고
    • Hamiltonian flows of curves in G/SO(n) and vector soliton equations of mKdV and sine-Gordon type
    • 2217753
    • S.C. Anco 2006 Hamiltonian flows of curves in G/SO(n) and vector soliton equations of mKdV and sine-Gordon type Symmetry Integrability Geom.: Methods Appl. (SIGMA) 2 044 2217753
    • (2006) Symmetry Integrability Geom.: Methods Appl. (SIGMA) , vol.2 , pp. 044
    • Anco, S.C.1
  • 18
    • 32944467597 scopus 로고    scopus 로고
    • Bi-Hamiltonian operators, integrable flows of curves using moving frames and geometric map equations
    • DOI 10.1088/0305-4470/39/9/005, PII S0305447006099859
    • S.C. Anco 2006 Bi-Hamiltonian operators, integrable flows of curves using moving frames, and geometric map equations J. Phys. A: Math. Gen. 39 2043 2072 1085.37049 10.1088/0305-4470/39/9/005 2211976 (Pubitemid 43260869)
    • (2006) Journal of Physics A: Mathematical and General , vol.39 , Issue.9 , pp. 2043-2072
    • Anco, S.C.1
  • 20
    • 41349116943 scopus 로고    scopus 로고
    • Deformation quantization of nonholonomic almost Kähler models and Einstein gravity
    • 10.1016/j.physleta.2008.01.044 2404752
    • S. Vacaru 2008 Deformation quantization of nonholonomic almost Kähler models and Einstein gravity Phys. Lett. A 372 2949 2955 10.1016/j.physleta.2008.01.044 2404752
    • (2008) Phys. Lett. A , vol.372 , pp. 2949-2955
    • Vacaru, S.1
  • 22
    • 0003320852 scopus 로고    scopus 로고
    • An introduction to Riemann-Finsler geometry
    • Springer Berlin 0954.53001
    • Bao, D., Chern, S.-S., Shen, Z.: An Introduction to Riemann-Finsler Geometry. Graduate Texts in Math., vol. 200. Springer, Berlin (2000)
    • (2000) Graduate Texts in Math. , vol.200
    • Bao, D.1    Chern, S.-S.2    Shen, Z.3
  • 23
    • 77149156146 scopus 로고
    • Sur les espaces non holonomes
    • G. Vranceanu 1926 Sur les espaces non holonomes C. R. Acad. Paris 103 852 854
    • (1926) C. R. Acad. Paris , vol.103 , pp. 852-854
    • Vranceanu, G.1
  • 24
  • 27
    • 0035877515 scopus 로고    scopus 로고
    • Locally anisotropic kinetic processes and thermodynamics in curved spaces
    • DOI 10.1006/aphy.2000.6121, PII S0003491600961219
    • S. Vacaru 2001 Locally anisotropic kinetic processes and thermodynamics in curved spaces Ann. Phys. (N.Y.) 290 83 123 1062.82047 10.1006/aphy.2000.6121 1834616 (Pubitemid 33377466)
    • (2001) Annals of Physics , vol.290 , Issue.2 , pp. 83-123
    • Vacaru, S.I.1
  • 28
    • 77952059792 scopus 로고    scopus 로고
    • Stochastic processes and thermodynamics on curved spaces
    • Special Issue
    • S. Vacaru 2000 Stochastic processes and thermodynamics on curved spaces Ann. Phys. (Leipzig) 9 175 176 Special Issue
    • (2000) Ann. Phys. (Leipzig) , vol.9 , pp. 175-176
    • Vacaru, S.1
  • 29
    • 56649083460 scopus 로고    scopus 로고
    • Curve flows in Lagrange-Finsler geometry, bi-Hamiltonian structures and solitons
    • doi: 10.1016/j.geomphys.2008.10.006
    • Anco, S., Vacaru, S.: Curve flows in Lagrange-Finsler geometry, bi-Hamiltonian structures and solitons. J. Geom. Phys. (2008). doi: 10.1016/j.geomphys.2008.10.006. math-ph/0609070
    • (2008) J. Geom. Phys.
    • Anco, S.1    Vacaru, S.2
  • 30
    • 77952014166 scopus 로고    scopus 로고
    • The entropy of Lagrange-Finsler spaces and Ricci flows
    • accepted
    • Vacaru, S.: The entropy of Lagrange-Finsler spaces and Ricci flows. Rep. Math. Phys. (2008, accepted). math.DG/0701621
    • (2008) Rep. Math. Phys.
    • Vacaru, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.