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Uspekhi Mat. Nauk, 2001, Volume 56, Issue 3(339), Pages 3–78 (Mi umn393)  

This article is cited in 12 scientific papers (total in 12 papers)

Isometric immersions of space forms into Riemannian and pseudo-Riemannian spaces of constant curvature

A. A. Borisenko

V. N. Karazin Kharkiv National University

Abstract: This survey contains results on local and global isometric immersions of two-dimensional and multidimensional Riemannian and pseudo-Riemannian space forms into spaces of constant sectional curvature.

DOI: https://doi.org/10.4213/rm393

Full text: PDF file (704 kB)
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English version:
Russian Mathematical Surveys, 2001, 56:3, 425–497

Bibliographic databases:

UDC: 514.763
MSC: Primary 57N35, 53C42; Secondary 53C21, 57R42, 53A35, 37K40
Received: 11.07.2000

Citation: A. A. Borisenko, “Isometric immersions of space forms into Riemannian and pseudo-Riemannian spaces of constant curvature”, Uspekhi Mat. Nauk, 56:3(339) (2001), 3–78; Russian Math. Surveys, 56:3 (2001), 425–497

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Qing Chen, Dafeng Zuo, Yi Cheng, “Isometric immersions of pseudo-Riemannian space forms”, J. Geom. Phys., 52:3 (2004), 241–262  crossref  mathscinet  zmath  adsnasa  isi  scopus
    2. Aledo J.A., Gálvez J.A., Pablo M., “Isometric immersions of $\mathbb L^2$ into $\mathbb L^4$”, Differential Geom. Appl., 24:6 (2006), 613–627  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. Rovenski V., “Submanifolds with restrictions on extrinsic $q$th scalar curvature”, Israel J. Math., 159:1 (2007), 289–316  crossref  mathscinet  zmath  isi  scopus
    4. Gálvez J.A., Mira P., “Isometric immersions of $\mathbb R^2$ into $\mathbb R^4$ and perturbation of Hopf tori”, Math. Z., 2009  crossref  mathscinet  isi  scopus
    5. Xia Qiaoling, “Ribaucour transformations for isometric immersions of pseudo-Riemannian space forms”, J. Geom. Phys., 59:6 (2009), 740–753  crossref  mathscinet  zmath  adsnasa  isi  scopus
    6. Michael T. Anderson, “Extension of symmetries on Einstein manifolds with boundary”, Sel math New ser, 2010  crossref  mathscinet  isi  scopus
    7. Khadjiev D., “On Invariants of Immersions of An N-Dimensional Manifold in An N-Dimensional Pseudo-Euclidean Space”, Journal of Nonlinear Mathematical Physics, 17, Suppl. 1 (2010), 49–70  crossref  mathscinet  zmath  adsnasa  isi  scopus
    8. Matthias Bergner, Lars Schäfer, “Isometric embedding of semi-Riemannian metrics into Minkowski space”, Analysis, 31:4 (2011), 313  crossref  mathscinet  zmath  scopus
    9. David Brander, Jun-ichi Inoguchi, Shimpei Kobayashi, “Constant Gaussian curvature surfaces in the 3-sphere via loop groups”, Pacific J. Math, 269:2 (2014), 281  crossref  mathscinet  zmath  isi
    10. Mirandola H., Vitorio F., “Global Isometric Embeddings of Multiple Warped Product Metrics Into Quadrics”, 38, no. 1, 2015, 119–134  mathscinet  zmath  isi
    11. Gromov M., “Geometric, algebraic, and analytic descendants of Nash isometric embedding theorems”, Bull. Amer. Math. Soc., 54:2 (2017), 173–245  crossref  mathscinet  zmath  isi  scopus
    12. Ay N., Jost J., VanLe H., Schwachhofer L., “Information Geometry”, Information Geometry, Ergebnisse der Mathematik und Iher Grenzgebiete 3 Folge, 64, Springer-Verlag Berlin, 2017, 1–407  crossref  mathscinet  isi
  • Успехи математических наук Russian Mathematical Surveys
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