논문KCI 등재
Seiberg-Witten-like equations on the strictly pseudoconvex $CR$-3 manifolds
대한수학회 (The Korean Mathematical Society)|2019.11|대한수학회보 (Bulletin of the KMS)|제56권 제6호|pp. 1551-1567|DOI 10.4134/BKMS.b181273
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
주제분류수학
초록
In this paper, Seiberg-Witten-like equations are written down on $3$-manifolds. Then, it has been proved that the $L^{2}$-solutions of these equations are trivial on $\mathbb{R}^3$. Finally, a global solution is obtained on the strictly pseudoconvex $CR$-3 manifolds for a given constant negative scalar curvature.
Abstract
In this paper, Seiberg-Witten-like equations are written down on $3$-manifolds. Then, it has been proved that the $L^{2}$-solutions of these equations are trivial on $\mathbb{R}^3$. Finally, a global solution is obtained on the strictly pseudoconvex $CR$-3 manifolds for a given constant negative scalar curvature.
참고문헌 (27)
- Helga Baum, "Lorentzian twistor spinors and CR-geometry", Differential Geometry and its Applications, 11(1), pp.69~96 (1999), Elsevier BV[DOI]
- D. E. Blair, "Riemannian geometry of contact and symplectic manifolds" (2002), Birkhauser Boston, Inc.
- A. L. CAREY, "Seiberg-Witten monopoles in three dimensions", Letters in Mathematical Physics, 39(3), pp.213~228 (1997), Springer Science and Business Media LLC[DOI]
- N. Degirmenci, "Seiberg-Witten-like equations on 6-dimensional SU(3)-manifolds", Balkan J. Geom. Appl, 20(2), pp.23~31 (2015)
- N. Degirmenci, "Seiberg-Witten-like equations on 7-manifolds with G2-structure", J. Nonlinear Math. Phys, 12(4), pp.457~461 (2005)
- S. Eker, "Seiberg-Witten equations on 8-dimensional manifolds with dierent self-duality", Balkan J. Geom. Appl, 22(2), pp.37~43 (2017)
- C. Fefferman, "Hp spaces of several variables", Acta Mathematica, 129(0), pp.137~193 (1972), International Press of Boston[DOI]
- T. Friedrich, "Dirac operators in Riemannian geometry" (2000), American Mathematical Society
- Troels Jorgensen, "Compact 3-Manifolds of Constant Negative Curvature Fibering Over the Circle", The Annals of Mathematics, 106(1), pp.61~ (1977), JSTOR[DOI]
- P. Kronheimer, "Monopoles and three-manifolds" (2007), Cambridge University Press
- H. B. Lawson, Jr., "Spin geometry" (1989), Princeton University Press
- undefined, "Some properties of conjugate functions.", Journal für die reine und angewandte Mathematik (Crelles Journal), 1932(167), pp.405~423 (1932), Walter de Gruyter GmbH[DOI]
- Joachim Lohkamp, "Metrics of Negative Ricci Curvature", The Annals of Mathematics, 140(3), pp.655~683 (1994), JSTOR[DOI]
- J. W. Morgan, "The Seiberg-Witten equations and applications to the topology of smooth four-manifolds" (1996), Princeton University Press
- Tomasz Mrowka, "Seiberg–Witten monopoles on Seifert fibered spaces", Communications in Analysis and Geometry, 5(4), pp.685~791 (1997), International Press of Boston[DOI]
- G. L. Naber, "Topology, geometry, and gauge elds" (1997), Springer-Verlag
- Timothy Nguyen, "The Seiberg–Witten equations on manifolds with boundary I: the space of monopoles and their boundary values", Communications in Analysis and Geometry, 20(3), pp.565~676 (2012), International Press of Boston[DOI]
- Liviu I. Nicolaescu, "Adiabatic limits of the Seiberg–Witten equations on Seifert manifolds", Communications in Analysis and Geometry, 6(2), pp.331~392 (1998), International Press of Boston[DOI]
- L. I. Nicolaescu, "Notes on Seiberg-Witten theory" (2000), American Mathematical Society
- Robert Petit, "Harmonic maps and strictly pseudoconvex CR manifolds", Communications in Analysis and Geometry, 10(3), pp.575~610 (2002), International Press of Boston[DOI]
- Robert Petit, "Spinc-structures and Dirac operators on contact manifolds", Differential Geometry and its Applications, 22(2), pp.229~252 (2005), Elsevier BV[DOI]
- D. Salamon, "Spin geometry and Seiberg-Witten invariants" (1996), Citeseer
- A. Shkheam, "Spaces of harmonic functions and harmonic quasiconformal mappings", Doctor, pp.2013
- A. I. Stipsicz, "Gauge theory and Stein llings of certain 3-manifolds", Turkish J. Math, 26(1), pp.115~130 (2002)
- Shukichi Tanno, "Variational Problems on Contact Riemannian Manifolds", Transactions of the American Mathematical Society, 314(1), pp.349~379 (1989), JSTOR[DOI]
- Clifford Henry Taubes, "The Seiberg–Witten equations and the Weinstein conjecture", Geometry & Topology, 11(4), pp.2117~2202 (2007), Mathematical Sciences Publishers[DOI]
- Edward Witten, "Monopoles and four-manifolds", Mathematical Research Letters, 1(6), pp.769~796 (1994), International Press of Boston[DOI]
관련 논문AI추천
RICCI CURVATURE AND MONOPOLE CLASSES ON 3-MANIFOLDSChanyoung Sung대한수학회 · 대한수학회지2012 · 제49권 제5호The Critical Point Equation on 3-dimensional α-cosymplectic ManifoldsAdara M. Blaga, Chiranjib Dey경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2020 · 제60권 제1호Miao-Tam equation on almost coK\"{a}hler manifoldsTarak Mandal대한수학회 · 대한수학회논문집2022 · 제37권 제3호On the closed Einstein-Weyl structure and compact $K$-contact manifoldAmalendu Ghosh대한수학회 · 대한수학회보2016 · 제53권 제6호A Note on Yamabe Solitons and Gradient Yamabe SolitonsKrishnendu De, Sujit Ghosh경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2022 · 제62권 제1호Homogeneity and symmetry on almost Kenmotsu $3$-manifoldsYaning Wang대한수학회 · 대한수학회지2019 · 제56권 제4호
이 간행물의 다른 논문 (17건)
Extension of phase-isometries between the unit spheres of atomic $L_p$-spaces for $p>0$Xujian Huang, Xihong Jinpp. 1377-1384Negacyclic codes of length $8p^s$ over $\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}$Jirayu Phuto, Chakkrid Klin-eampp. 1385-1422Riemann-Liouville fractional fundamental theorem of calculus and Riemann-Liouville fractional Polya type integral inequality and its extension to Choquet integral settingGeorge A. Anastassioupp. 1423-1433Reliability analysis of checkpointing model with multiple verification mechanism이유태pp. 1435-1445Mild solutions for the relativistic Vlasov-Klein-Gordon systemXianwen Zhang, Meixia Xiaopp. 1447-1465
