Null curves and hypersurfaces of semi-Riemannian manifolds /

Null curves and hypersurfaces of semi-Riemannian manifolds /

Saved in:
Bibliographic Details
Author / Creator:Duggal, Krishan L., 1929-
Imprint:Singapore ; Hackensack, NJ : World Scientific, 2007.
Description:viii, 293 p. ; 26 cm.
Language:English
Subject:
Riemannian manifolds.
Hypersurfaces.
Geometry, Differential.
Geometry, Differential.
Hypersurfaces.
Riemannian manifolds.
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/6643861
Hidden Bibliographic Details
Other authors / contributors:Jin, Dae Ho
ISBN:9789812706478
981270647X
Notes:Includes bibliographical references (p. 281-287) and index.
Summary:"This is a first textbook that is entirely focused on the up-to-date developments of null curves with their applications to science and engineering. It fills an important gap in a second-level course in differential geometry, as well as being essential for a core undergraduate course on Riemannian curves and surfaces. The sequence of chapters is arranged to provide in-depth understanding of a chapter and stimulate further interest in the next. The book comprises a large variety of solved examples and rigorous exercises that range from elementary to higher levels. This unique volume is self-contained and unified in presenting: a systematic account of all possible null curves, their Frenet equations, unique null Cartan curves in Lorentzian manifolds and their practical problems in science and engineering; and the geometric and physical significance of null geodesics, mechanical systems involving curvature of null curves, simple variation problems and the interrelation of null curves with hypersurfaces."--BOOK JACKET.

MARC

LEADER 00000cam a2200000Ia 4500
001 6643861
005 20130306135900.0
008 070406s2007 si b 001 0 eng d
003 ICU
010 |a  2011284437 
020 |a 9789812706478 
020 |a 981270647X 
035 |a (OCoLC)154672020 
035 |a yb989423 
040 |a BTCTA  |b eng  |c BTCTA  |d YDXCP  |d BAKER  |d UUM  |d MUM  |d DEBBG  |d DEBSZ  |d DLC  |d HDC  |d OCLCO  |d MUU 
049 |a CGUA 
050 4 |a QA649  |b .D84 2007 
084 |a SK 370  |2 rvk 
084 |a 53-02  |a 53C50  |a 53C40  |2 msc 
100 1 |a Duggal, Krishan L.,  |d 1929-  |0 http://id.loc.gov/authorities/names/n94047699  |1 http://viaf.org/viaf/278236832 
245 1 0 |a Null curves and hypersurfaces of semi-Riemannian manifolds /  |c Krishan L. Duggal, Dae Ho Jin. 
260 |a Singapore ;  |a Hackensack, NJ :  |b World Scientific,  |c 2007. 
300 |a viii, 293 p. ;  |c 26 cm. 
336 |a text  |b txt  |2 rdacontent  |0 http://id.loc.gov/vocabulary/contentTypes/txt 
337 |a unmediated  |b n  |2 rdamedia  |0 http://id.loc.gov/vocabulary/mediaTypes/n 
338 |a volume  |b nc  |2 rdacarrier  |0 http://id.loc.gov/vocabulary/carriers/nc 
504 |a Includes bibliographical references (p. 281-287) and index. 
505 0 0 |g 1  |t The concept of null curves  |g 1 --  |g 1.1  |t Smooth manifolds  |g 1 --  |g 1.2  |t Semi-Riemannian manifolds  |g 5 --  |g 1.4  |t Screen and null transversal bundles  |g 9 --  |g 1.5  |t Quasi-orthonormal basis along a null curve  |g 10 --  |g 1.6  |t Brief notes and exercises  |g 14 --  |g 2  |t Null curves in Lorentzian manifolds [Characters not reproducible]  |g 19 --  |g 2.1  |t Frenet frames along null curves  |g 19 --  |g 2.2  |t Invariance of Frenet frames  |g 25 --  |g 2.3  |t Null Cartan curves in [Characters not reproducible], [Characters not reproducible] and [Characters not reproducible]  |g 29 --  |g 2.4  |t Null Cartan curves in [Characters not reproducible]  |g 35 --  |g 2.5  |t Fundamental theorem of null curves in [Characters not reproducible]  |g 42 --  |g 2.6  |t Brief notes and exercises  |g 45 --  |g 3  |t Null curves in [Characters not reproducible]  |g 51 --  |g 3.1  |t Type 1 general Frenet frames  |g 52 --  |g 3.2  |t Type 2 general Frenet frames  |g 55 --  |g 3.3  |t Natural Frenet equations  |g 63 --  |g 3.4  |t Invariance of Frenet equations  |g 74 --  |g 3.5  |t Geometry of null curves in [Characters not reproducible]  |g 81 --  |g 3.6  |t Geometry of null curves in [Characters not reproducible]  |g 86 --  |g 3.7  |t Fundamental theorem of null curves in [Characters not reproducible]  |g 91 --  |g 3.8  |t Brief notes and exercises  |g 95 --  |g 4  |t Null curves in [Characters not reproducible]  |g 97 --  |g 4.1  |t Frenet equations of Type 1 and Type 2  |g 97 --  |g 4.2  |t Frenet equations of Type q ([greater than or equal] 3)  |g 100 --  |g 4.3  |t Natural Frenet equations  |g 108 --  |g 4.4  |t Invariance of Frenet frames  |g 119 --  |g 4.5  |t Geometry of null curves in [Characters not reproducible]  |g 129 --  |g 4.6  |t Fundamental theorem of null curves in [Characters not reproducible]  |g 135 --  |g 5  |t Geometry of null Cartan curves  |g 141 --  |g 5.1  |t Null Cartan curves in Lorentzian manifolds  |g 141 --  |g 5.2  |t Null Cartan helices  |g 146 --  |g 5.3  |t Brief notes and research problems  |g 157 --  |g 6  |t Applications of null curves  |g 165 --  |g 6.1  |t Soliton solutions in 3D Lorentzian space forms  |g 165 --  |g 6.2  |t Soliton solutions in Minkowski spaces  |g 169 --  |g 6.3  |t Mechanical systems and 3D null curves  |g 173 --  |g 7  |t Lightlike hypersurfaces  |g 185 --  |g 7.2  |t Screen and transversal bundles  |g 190 --  |g 7.3  |t Lightlike second fundamental forms  |g 198 --  |g 7.4  |t Integrable screen distribution  |g 210 --  |g 7.5  |t Induced curvature and Ricci tensors  |g 220 --  |g 7.6  |t Scalar curvature of genus zero  |g 232 --  |g 7.7  |t Brief notes and exercises  |g 235 --  |g 8  |t Geometry and physics of null geodesics  |g 241 --  |g 8.2  |t Globally null manifolds  |g 246 --  |g 8.3  |t Frenet frames along null geodesics  |g 252 --  |g 8.4  |t Scalar curvature and null warped products  |g 263 --  |g 8.5  |t Null geodesics and photon surfaces  |g 268 --  |g 8.6  |t Brief notes on research papers  |g 275. 
520 1 |a "This is a first textbook that is entirely focused on the up-to-date developments of null curves with their applications to science and engineering. It fills an important gap in a second-level course in differential geometry, as well as being essential for a core undergraduate course on Riemannian curves and surfaces. The sequence of chapters is arranged to provide in-depth understanding of a chapter and stimulate further interest in the next. The book comprises a large variety of solved examples and rigorous exercises that range from elementary to higher levels. This unique volume is self-contained and unified in presenting: a systematic account of all possible null curves, their Frenet equations, unique null Cartan curves in Lorentzian manifolds and their practical problems in science and engineering; and the geometric and physical significance of null geodesics, mechanical systems involving curvature of null curves, simple variation problems and the interrelation of null curves with hypersurfaces."--BOOK JACKET. 
650 0 |a Riemannian manifolds.  |0 http://id.loc.gov/authorities/subjects/sh85114045 
650 0 |a Hypersurfaces.  |0 http://id.loc.gov/authorities/subjects/sh85063722 
650 0 |a Geometry, Differential.  |0 http://id.loc.gov/authorities/subjects/sh85054146 
650 0 7 |a Differentialgeometrie.  |2 swd 
650 0 7 |a Hyperfläche.  |2 swd 
650 0 7 |a Pseudo-Riemannscher Raum.  |2 swd 
650 7 |a Geometry, Differential.  |2 fast  |0 http://id.worldcat.org/fast/fst00940919 
650 7 |a Hypersurfaces.  |2 fast  |0 http://id.worldcat.org/fast/fst00965830 
650 7 |a Riemannian manifolds.  |2 fast  |0 http://id.worldcat.org/fast/fst01097804 
700 1 |a Jin, Dae Ho  |0 http://id.loc.gov/authorities/names/no2008009883  |1 http://viaf.org/viaf/73652836 
903 |a HeVa 
929 |a cat 
999 f f |i 16efd6cf-3823-58d6-8079-c1f180303d9c  |s ae7bc147-b83f-5a3e-9551-8e554ddea192 
928 |t Library of Congress classification  |a QA670 .D84 2007  |l ASR  |c ASR-SciASR  |i 5159209 
927 |t Library of Congress classification  |a QA670 .D84 2007  |l ASR  |c ASR-SciASR  |e VAND  |e CRERAR  |b 80480393  |i 8297006 
Purchased from The Ed & Martha Vanderwicken Book Fund bookplate
The John Crerar Library bookplate

Similar Items