Book Review
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MathSciNet review:
3363150
Full text of review:
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Book Information:
Author:
Alexander Isaev
Title:
Spherical tube hypersurfaces
Additional book information:
Lecture Notes in Mathematics, Vol. 2020,
Springer,
Heidelberg,
2011,
xii+220 pp.,
ISBN 978-3-642-19782-6
M. Salah Baouendi, Peter Ebenfelt, and Linda Preiss Rothschild, Real submanifolds in complex space and their mappings, Princeton Mathematical Series, vol. 47, Princeton University Press, Princeton, NJ, 1999. MR 1668103, DOI 10.1515/9781400883967
Albert Boggess, CR manifolds and the tangential Cauchy-Riemann complex, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1991. MR 1211412
John P. D’Angelo, Several complex variables and the geometry of real hypersurfaces, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1993. MR 1224231
John P. D’Angelo and Jeremy T. Tyson, An invitation to Cauchy-Riemann and sub-Riemannian geometries, Notices Amer. Math. Soc. 57 (2010), no. 2, 208–219. MR 2604488
Sorin Dragomir and Giuseppe Tomassini, Differential geometry and analysis on CR manifolds, Progress in Mathematics, vol. 246, Birkhäuser Boston, Inc., Boston, MA, 2006. MR 2214654, DOI 10.1007/0-8176-4483-0
Vladimir Ezhov, Ben McLaughlin, and Gerd Schmalz, From Cartan to Tanaka: getting real in the complex world, Notices Amer. Math. Soc. 58 (2011), no. 1, 20–27. MR 2777590
Thomas Garrity and Zachary Grossman, On relations of invariants for vector-valued forms, Electron. J. Linear Algebra 11 (2004), 24–40. MR 2033475, DOI 10.13001/1081-3810.1119
Thomas Garrity and Robert Mizner, Invariants of vector-valued bilinear and sesquilinear forms, Linear Algebra Appl. 218 (1995), 225–237. MR 1324060, DOI 10.1016/0024-3795(93)00174-X
Thomas Garrity and Robert Mizner, The equivalence problem for higher-codimensional CR structures, Pacific J. Math. 177 (1997), no. 2, 211–235. MR 1444781, DOI 10.2140/pjm.1997.177.211
Xiaojun Huang, Local equivalence problems for real submanifolds in complex spaces, Real methods in complex and CR geometry, Lecture Notes in Math., vol. 1848, Springer, Berlin, 2004, pp. 109–163. MR 2087582, DOI 10.1007/978-3-540-44487-9_{3}
Thomas A. Ivey and J. M. Landsberg, Cartan for beginners: differential geometry via moving frames and exterior differential systems, Graduate Studies in Mathematics, vol. 61, American Mathematical Society, Providence, RI, 2003. MR 2003610, DOI 10.1090/gsm/061
Howard Jacobowitz, An introduction to CR structures, Mathematical Surveys and Monographs, vol. 32, American Mathematical Society, Providence, RI, 1990. MR 1067341, DOI 10.1090/surv/032
Steven G. Krantz, Function theory of several complex variables, AMS Chelsea Publishing, Providence, RI, 2001. Reprint of the 1992 edition. MR 1846625, DOI 10.1090/chel/340
Robert I. Mizner, CR structures of codimension $2$, J. Differential Geom. 30 (1989), no. 1, 167–190. MR 1001274
Frank Morgan, Riemannian geometry, 2nd ed., A K Peters, Ltd., Wellesley, MA, 1998. A beginner’s guide. MR 1600519
François Treves, A treasure trove of geometry and analysis: the hyperquadric, Notices Amer. Math. Soc. 47 (2000), no. 10, 1246–1256. MR 1784240
S. M. Webster, Pseudo-Hermitian structures on a real hypersurface, J. Differential Geometry 13 (1978), no. 1, 25–41. MR 520599
P. C. Yang, Automorphism of tube domains, Amer. J. Math. 104 (1982), no. 5, 1005–1024. MR 675307, DOI 10.2307/2374081
References
- M. Salah Baouendi, Peter Ebenfelt, and Linda Preiss Rothschild, Real submanifolds in complex space and their mappings, Princeton Mathematical Series, vol. 47, Princeton University Press, Princeton, NJ, 1999. MR 1668103 (2000b:32066)
- Albert Boggess, CR manifolds and the tangential Cauchy-Riemann complex, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1991. MR 1211412 (94e:32035)
- John P. D’Angelo, Several complex variables and the geometry of real hypersurfaces, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1993. MR 1224231 (94i:32022)
- John P. D’Angelo and Jeremy T. Tyson, An invitation to Cauchy-Riemann and sub-Riemannian geometries, Notices Amer. Math. Soc. 57 (2010), no. 2, 208–219. MR 2604488 (2011b:32055)
- Sorin Dragomir and Giuseppe Tomassini, Differential geometry and analysis on CR manifolds, Progress in Mathematics, vol. 246, Birkhäuser Boston Inc., Boston, MA, 2006. MR 2214654 (2007b:32056)
- Vladimir Ezhov, Ben McLaughlin, and Gerd Schmalz, From Cartan to Tanaka: getting real in the complex world, Notices Amer. Math. Soc. 58 (2011), no. 1, 20–27. MR 2777590
- Thomas Garrity and Zachary Grossman, On relations of invariants for vector-valued forms, Electron. J. Linear Algebra 11 (2004), 24–40. MR 2033475 (2004k:15056)
- Thomas Garrity and Robert Mizner, Invariants of vector-valued bilinear and sesquilinear forms, Linear Algebra Appl. 218 (1995), 225–237. MR 1324060 (96d:15044), DOI 10.1016/0024-3795(93)00174-X
- Thomas Garrity and Robert Mizner, The equivalence problem for higher-codimensional CR structures, Pacific J. Math. 177 (1997), no. 2, 211–235. MR 1444781 (99b:32007), DOI 10.2140/pjm.1997.177.211
- Xiaojun Huang, Local equivalence problems for real submanifolds in complex spaces, Real methods in complex and CR geometry, Lecture Notes in Math., vol. 1848, Springer, Berlin, 2004, pp. 109–163. MR 2087582 (2005j:32041), DOI 10.1007/978-3-540-44487-9_3
- Thomas A. Ivey and J. M. Landsberg, Cartan for beginners: differential geometry via moving frames and exterior differential systems, Graduate Studies in Mathematics, vol. 61, American Mathematical Society, Providence, RI, 2003. MR 2003610 (2004g:53002)
- Howard Jacobowitz, An introduction to CR structures, Mathematical Surveys and Monographs, vol. 32, American Mathematical Society, Providence, RI, 1990. MR 1067341 (93h:32023)
- Steven G. Krantz, Function theory of several complex variables, AMS Chelsea Publishing, Providence, RI, 2001. Reprint of the 1992 edition. MR 1846625 (2002e:32001)
- Robert I. Mizner, CR structures of codimension $2$, J. Differential Geom. 30 (1989), no. 1, 167–190. MR 1001274 (90h:32046)
- Frank Morgan, Riemannian geometry, 2nd ed., A K Peters Ltd., Wellesley, MA, 1998. A beginner’s guide. MR 1600519 (98i:53001)
- François Treves, A treasure trove of geometry and analysis: the hyperquadric, Notices Amer. Math. Soc. 47 (2000), no. 10, 1246–1256. MR 1784240 (2001h:32056)
- S. M. Webster, Pseudo-Hermitian structures on a real hypersurface, J. Differential Geom. 13 (1978), no. 1, 25–41. MR 520599 (80e:32015)
- P. C. Yang, Automorphism of tube domains, Amer. J. Math. 104 (1982), no. 5, 1005–1024. MR 675307 (84b:32038), DOI 10.2307/2374081
Review Information:
Reviewer:
Thomas Garrity
Affiliation:
Williams College
Email:
tgarrity@williams.edu
Journal:
Bull. Amer. Math. Soc.
51 (2014), 675-685
DOI:
https://doi.org/10.1090/S0273-0979-2014-01446-6
Published electronically:
May 19, 2014
Review copyright:
© Copyright 2014
American Mathematical Society
