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Mat. Sb., 2004, Volume 195, Number 1, Pages 89–102 (Mi msb794)  

This article is cited in 28 scientific papers (total in 28 papers)

New examples of Hamilton-minimal and minimal Lagrangian manifolds in $\mathbb C^n$ and $\mathbb C\mathrm P^n$

A. E. Mironov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: A new method is proposed for constructing Hamilton-minimal and minimal Lagrangian immersions and embeddings of manifolds in $\mathbb C^n$ and in $\mathbb C\mathrm P^n$. In particular, using this method it is possible to construct embeddings of manifolds such as the $(2n+1)$-dimensional generalized Klein bottle $\mathscr K^{2n+1}$, $S^{2n+1}\times S^1$, $\mathscr K^{2n+1}\times S^1$, $S^{2n+1}\times S^1\times S^1$, and others.


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English version:
Sbornik: Mathematics, 2004, 195:1, 85–96

Bibliographic databases:

UDC: 514.76
MSC: Primary 53D12; Secondary 57N35, 57R17
Received: 15.01.2003

Citation: A. E. Mironov, “New examples of Hamilton-minimal and minimal Lagrangian manifolds in $\mathbb C^n$ and $\mathbb C\mathrm P^n$”, Mat. Sb., 195:1 (2004), 89–102; Sb. Math., 195:1 (2004), 85–96

Citation in format AMSBIB
\by A.~E.~Mironov
\paper New examples of Hamilton-minimal and minimal Lagrangian manifolds in~$\mathbb C^n$ and~$\mathbb C\mathrm P^n$
\jour Mat. Sb.
\yr 2004
\vol 195
\issue 1
\pages 89--102
\jour Sb. Math.
\yr 2004
\vol 195
\issue 1
\pages 85--96

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    This publication is cited in the following articles:
    1. A. E. Mironov, “Ierarkhiya uravnenii Veselova–Novikova i integriruemye deformatsii minimalnykh lagranzhevykh torov v $\mathbb CP^2$”, Sib. elektron. matem. izv., 1 (2004), 38–46  mathnet  mathscinet  zmath
    2. Ma Hui, Schmies M., “Examples of Hamiltonian stationary Lagrangian tori in $\mathbb C\mathrm P^2$”, Geom. Dedicata, 118:1 (2006), 173–183  crossref  mathscinet  zmath  isi
    3. Castro I., Li Haizhong, Urbano F., “Hamiltonian-minimal Lagrangian submanifolds in complex space forms”, Pacific J. Math., 227:1 (2006), 43–63  crossref  mathscinet  zmath  isi
    4. A. E. Mironov, “On a Family of Conformally Flat Minimal Lagrangian Tori in $\mathbb CP^3$”, Math. Notes, 81:3 (2007), 329–337  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. A. E. Mironov, “Spectral Data for Hamiltonian-Minimal Lagrangian Tori in $\mathbb C\mathrm P^2$”, Proc. Steklov Inst. Math., 263 (2008), 112–126  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    6. Mironov A.E., Zuo Dafeng, “On a family of conformally flat Hamiltonian-minimal Lagrangian tori in $\mathbb{CP}^3$”, Int. Math. Res. Not. IMRN, 2008, rnn078, 13 pp.  mathscinet  zmath  isi
    7. I. P. Rybnikov, “Minimal Lagrangian submanifolds in $\mathbb C\mathrm P^n$ with diagonal metric”, Siberian Math. J., 52:1 (2011), 105–112  mathnet  crossref  mathscinet  isi
    8. Henri Anciaux, Ildefonso Castro, “Construction of Hamiltonian-Minimal Lagrangian submanifolds in Complex Euclidean Space”, Results. Math, 2011  crossref  mathscinet  isi
    9. Hunter R., McIntosh I., “The classification of Hamiltonian stationary Lagrangian tori in CP2 by their spectral data”, Manuscripta Math, 135:3–4 (2011), 437–468  crossref  mathscinet  zmath  isi  elib
    10. Chen Q., Hu S., Xu X., “Construction of Lagrangian Submanifolds in CPN”, Pac. J. Math., 258:1 (2012), 31–49  crossref  mathscinet  zmath  isi  elib
    11. A. E. Mironov, T. E. Panov, “Hamiltonian-minimal Lagrangian submanifolds in toric varieties”, Russian Math. Surveys, 68:2 (2013), 392–394  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    12. A. E. Mironov, T. E. Panov, “Intersections of Quadrics, Moment-Angle Manifolds, and Hamiltonian-Minimal Lagrangian Embeddings”, Funct. Anal. Appl., 47:1 (2013), 38–49  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    13. T. E. Panov, “Geometric structures on moment-angle manifolds”, Russian Math. Surveys, 68:3 (2013), 503–568  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    14. A. V. Penskoi, “Extremal metrics for eigenvalues of the Laplace–Beltrami operator on surfaces”, Russian Math. Surveys, 68:6 (2013), 1073–1130  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    15. Penskoi A.V., “Generalized Lawson Tori and Klein Bottles”, J. Geom. Anal., 25:4 (2015), 2645–2666  crossref  mathscinet  zmath  isi  elib
    16. Karpukhin M., “Spectral Properties of a Family of Minimal Tori of Revolution in the Five-Dimensional Sphere”, Can. Math. Bul.-Bul. Can. Math., 58:2 (2015), 285–296  crossref  mathscinet  zmath  isi
    17. Broderick Causley, “Bipolar Lawson Tau-Surfaces and Generalized Lawson Tau-Surfaces”, SIGMA, 12 (2016), 009, 11 pp.  mathnet  crossref
    18. B. T. Saparbayeva, “On the Schrödinger operator connected with a family of Hamiltonian-minimal Lagrangian surfaces in $\mathbb CP^2$”, Siberian Math. J., 57:6 (2016), 1077–1081  mathnet  crossref  crossref  isi  elib
    19. Yamamoto H., “Weighted Hamiltonian stationary Lagrangian submanifolds and generalized Lagrangian mean curvature flows in toric almost Calabi-Yau manifolds”, Tohoku Math. J., 68:3 (2016), 329–347  crossref  mathscinet  zmath  isi
    20. V. M. Buchstaber, N. Yu. Erokhovets, M. Masuda, T. E. Panov, S. Park, “Cohomological rigidity of manifolds defined by 3-dimensional polytopes”, Russian Math. Surveys, 72:2 (2017), 199–256  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    21. N. A. Tyurin, “Pseudotoric structures: Lagrangian submanifolds and Lagrangian fibrations”, Russian Math. Surveys, 72:3 (2017), 513–546  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    22. Luo Y., “Contact Stationary Legendrian Surfaces in S-5”, Pac. J. Math., 293:1 (2018), 101–120  crossref  mathscinet  zmath  isi
    23. Ma H., Mironov A.E., Zuo D., “An Energy Functional For Lagrangian Tori in Cp2”, Ann. Glob. Anal. Geom., 53:4 (2018), 583–595  crossref  mathscinet  zmath  isi
    24. M. S. Yermentay, “On minimal isotropic tori in $\mathbb CP^3$”, Siberian Math. J., 59:3 (2018), 415–419  mathnet  crossref  crossref  isi  elib
    25. A. A. Kazhymurat, “On a lower bound for the energy functional on a family of Hamiltonian minimal Lagrangian tori in $\mathbb CP^2$”, Siberian Math. J., 59:4 (2018), 641–647  mathnet  crossref  crossref  isi  elib
    26. M. A. Ovcharenko, “On Hamiltonian-minimal isotropic homogeneous tori in $\mathbb C^n$ and $\mathbb C\mathrm P^n$”, Siberian Math. J., 59:5 (2018), 931–937  mathnet  crossref  crossref  isi  elib
    27. M. S. Ermentai, “Ob odnom semeistve minimalnykh izotropnykh torov i butylok Kleina v $\mathbb{C}P^3$”, Sib. elektron. matem. izv., 16 (2019), 955–958  mathnet  crossref
    28. M. A. Ovcharenko, “On Hamiltonian Minimality of Isotropic Nonhomogeneous Tori in $\mathbb{H}^n$ and $\mathbb C\mathrm P^{2n+1}$”, Math. Notes, 108:1 (2020), 108–116  mathnet  crossref  crossref  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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