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Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh.:
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Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh., 1989, Volume 35, Pages 179–239 (Mi intd118)  

This article is cited in 9 scientific papers (total in 9 papers)

Quadratic mappings and smooth vector functions: Euler characteristics of level sets

A. A. Agrachev, R. V. Gamkrelidze


Abstract: Quadratic maps of $R^N$ into $R^K$ are studied. Explicit expressions are obtained for the Euler characteristics of level sets of such maps. The Euler characteristics of level sets of smooth vector-valued functions are also evaluated in terms of their values at critical points.

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English version:
Journal of Soviet Mathematics, 1991, 55:4, 1892–1928

Bibliographic databases:

Document Type: Article
UDC: 517.974+515.164.152+515.164.174

Citation: A. A. Agrachev, R. V. Gamkrelidze, “Quadratic mappings and smooth vector functions: Euler characteristics of level sets”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh., 35, VINITI, Moscow, 1989, 179–239; J. Soviet Math., 55:4 (1991), 1892–1928

Citation in format AMSBIB
\Bibitem{AgrGam89}
\by A.~A.~Agrachev, R.~V.~Gamkrelidze
\paper Quadratic mappings and smooth vector functions: Euler characteristics of level sets
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh.
\yr 1989
\vol 35
\pages 179--239
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/intd118}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1012331}
\zmath{https://zbmath.org/?q=an:0727.58009|0719.58013}
\transl
\jour J. Soviet Math.
\yr 1991
\vol 55
\issue 4
\pages 1892--1928
\crossref{https://doi.org/10.1007/BF01095139}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. D. Kovalev, “Quadratic and Rigidity Mappings”, Proc. Steklov Inst. Math., 239 (2002), 184–201  mathnet  mathscinet  zmath
    2. M. D. Kovalev, “Straightened hinged frameworks”, Sb. Math., 195:6 (2004), 833–858  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. T. M. Aliashvili, G. N. Khimshiashvili, “On the Euler characteristic of an intersection of quadrics”, Russian Math. Surveys, 61:3 (2006), 551–552  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. V. A. Krasnov, “Real three-dimensional biquadrics”, Izv. Math., 74:4 (2010), 781–804  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. V. A. Krasnov, “Real four-dimensional biquadrics”, Izv. Math., 75:2 (2011), 371–394  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. V. A. Krasnov, “Real $GM$-Biquadrics”, Math. Notes, 89:6 (2011), 830–838  mathnet  crossref  crossref  mathscinet  isi
    7. D. Yu. Karamzin, “The Dines theorem and some other properties of quadratic mappings”, Comput. Math. Math. Phys., 55:10 (2015), 1633–1641  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    8. A. V. Arutyunov, S. E. Zhukovskiy, “Properties of surjective real quadratic maps”, Sb. Math., 207:9 (2016), 1187–1214  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    9. V. A. Krasnov, “On intersections of two real quadrics”, Izv. Math., 82:1 (2018), 91–139  mathnet  crossref  crossref  adsnasa  isi  elib
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