Introduction to Lorentz geometry : curves and surfaces / Ivo Terek Couto, Alexandre Lymberopoulos.
Couto, Ivo Terek| Call Number | 516.36 |
| Author | Couto, Ivo Terek, author. |
| Title | Introduction to Lorentz geometry : curves and surfaces / Ivo Terek Couto, Alexandre Lymberopoulos. |
| Edition | 1st. |
| Physical Description | 1 online resource : illustrations (black and white) |
| Notes | Translated from the Portuguese. <P>1. Welcome to Lorentz-Minkowski Space. 1.1. Pseudo-Euclidean Spaces. 1.2. Subspaces of<STRONG> RQe</STRONG>. 1.3. Contextualization in Special Relativity. 1.4. Isometries in RQe. 1.5. Investigating O1(2, <B>R</B>) And O1(3, <B>R</B>). 1.6 Cross Product in <STRONG>RQe</STRONG>. 2. Local Theory of Curves. 2.1. Parametrized Curves in <STRONG>RQe</STRONG>. 2.2. Curves in the Plane. 2.3. Curves in Space. 3. Surfaces in Space. 3.1. Basic Topology of Surfaces. 3.2. Casual type of Surfaces, First Fundamental Form. 3.3. Second Fundamental Form and Curvatures. 3.4. The Diagonalization Problem. 3.5. Curves in Surface. 3.6. Geodesics, Variational Methods and Energy. 3.7. The Fundamental Theorem of Surfaces. 4. Abstract Surfaces and Further Topics. 4.1. Pseudo-Riemannian Metrics. 4.2. Riemann's Classification Theorem. 4.3. Split-Complex Numbers and Critical Surfaces. 4.4 Digression: Completeness and Causality</P> |
| Summary | Lorentz Geometry is a very important intersection between Mathematics and Physics, being the mathematical language of General Relativity. Learning this type of geometry is the first step in properly understanding questions regarding the structure of the universe, such as: What is the shape of the universe? What is a spacetime? What is the relation between gravity and curvature? Why exactly is time treated in a different manner than other spatial dimensions? Introduction to Lorentz Geometry: Curves and Surfaces intends to provide the reader with the minimum mathematical background needed to pursue these very interesting questions, by presenting the classical theory of curves and surfaces in both Euclidean and Lorentzian ambient spaces simultaneously. Features: Over 300 exercises Suitable for senior undergraduates and graduates studying Mathematics and Physics Written in an accessible style without loss of precision or mathematical rigor Solution manual available on www.routledge.com/9780367468644 |
| Added Author | Lymberopoulos, Alexandre, author. |
| Subject | GEOMETRY, DIFFERENTIAL. LORENTZ TRANSFORMATIONS. CURVES. SURFACES. MATHEMATICAL PHYSICS. MATHEMATICS / Arithmetic SCIENCE / Mathematical Physics MATHEMATICS / Geometry / General |
| Multimedia |
Total Ratings:
0
04100cam a22006491i 4500
001
vtls001594539
003
VRT
005
20220808223500.0
006
m d
007
cr |||||||||||
008
220808s2020 flua ob 001 0 eng d
020
$a 9781000223361 $q (ePub ebook)
020
$a 1000223361
020
$a 9781000223347 $q (PDF ebook)
020
$a 1000223345
020
$a 9781000223354 $q (Mobipocket ebook)
020
$a 1000223353
020
$a 9781003031574 $q (ebook)
020
$a 1003031579
020
$z 9780367468644 (hbk.)
024
7
$a 10.1201/9781003031574 $2 doi
035
$a (OCoLC)1233321295
035
$a (OCoLC-P)1233321295
035
$a (FlBoTFG)9781003031574
039
9
$y 202208082235 $z santha
040
$a OCoLC-P $b eng $e rda $e pn $c OCoLC-P
050
4
$a QA641
072
7
$a MAT $x 004000 $2 bisacsh
072
7
$a SCI $x 040000 $2 bisacsh
072
7
$a MAT $x 012000 $2 bisacsh
072
7
$a PHU $2 bicssc
082
0
4
$a 516.36 $2 23
100
1
$a Couto, Ivo Terek, $e author.
245
1
0
$a Introduction to Lorentz geometry : $b curves and surfaces / $c Ivo Terek Couto, Alexandre Lymberopoulos.
250
$a 1st.
264
1
$a Boca Raton : $b Chapman & Hall/CRC, $c 2020.
300
$a 1 online resource : $b illustrations (black and white)
336
$a text $2 rdacontent
336
$a still image $2 rdacontent
337
$a computer $2 rdamedia
338
$a online resource $2 rdacarrier
500
$a Translated from the Portuguese.
500
$a <P>1. Welcome to Lorentz-Minkowski Space. 1.1. Pseudo-Euclidean Spaces. 1.2. Subspaces of<STRONG> RQe</STRONG>. 1.3. Contextualization in Special Relativity. 1.4. Isometries in RQe. 1.5. Investigating O1(2, <B>R</B>) And O1(3, <B>R</B>). 1.6 Cross Product in <STRONG>RQe</STRONG>. 2. Local Theory of Curves. 2.1. Parametrized Curves in <STRONG>RQe</STRONG>. 2.2. Curves in the Plane. 2.3. Curves in Space. 3. Surfaces in Space. 3.1. Basic Topology of Surfaces. 3.2. Casual type of Surfaces, First Fundamental Form. 3.3. Second Fundamental Form and Curvatures. 3.4. The Diagonalization Problem. 3.5. Curves in Surface. 3.6. Geodesics, Variational Methods and Energy. 3.7. The Fundamental Theorem of Surfaces. 4. Abstract Surfaces and Further Topics. 4.1. Pseudo-Riemannian Metrics. 4.2. Riemann's Classification Theorem. 4.3. Split-Complex Numbers and Critical Surfaces. 4.4 Digression: Completeness and Causality</P>
520
$a Lorentz Geometry is a very important intersection between Mathematics and Physics, being the mathematical language of General Relativity. Learning this type of geometry is the first step in properly understanding questions regarding the structure of the universe, such as: What is the shape of the universe? What is a spacetime? What is the relation between gravity and curvature? Why exactly is time treated in a different manner than other spatial dimensions? Introduction to Lorentz Geometry: Curves and Surfaces intends to provide the reader with the minimum mathematical background needed to pursue these very interesting questions, by presenting the classical theory of curves and surfaces in both Euclidean and Lorentzian ambient spaces simultaneously. Features: Over 300 exercises Suitable for senior undergraduates and graduates studying Mathematics and Physics Written in an accessible style without loss of precision or mathematical rigor Solution manual available on www.routledge.com/9780367468644
588
$a OCLC-licensed vendor bibliographic record.
650
0
$a GEOMETRY, DIFFERENTIAL.
650
0
$a LORENTZ TRANSFORMATIONS.
650
0
$a CURVES.
650
0
$a SURFACES.
650
0
$a MATHEMATICAL PHYSICS.
650
7
$a MATHEMATICS / Arithmetic $2 bisacsh
650
7
$a SCIENCE / Mathematical Physics $2 bisacsh
650
7
$a MATHEMATICS / Geometry / General $2 bisacsh
700
1
$a Lymberopoulos, Alexandre, $e author.
856
4
0
$3 Taylor & Francis $u https://www.taylorfrancis.com/books/9781003031574
856
4
2
$3 OCLC metadata license agreement $u http://www.oclc.org/content/dam/oclc/forms/terms/vbrl-201703.pdf
999
$a VIRTUA
No Reviews to Display
| Summary | Lorentz Geometry is a very important intersection between Mathematics and Physics, being the mathematical language of General Relativity. Learning this type of geometry is the first step in properly understanding questions regarding the structure of the universe, such as: What is the shape of the universe? What is a spacetime? What is the relation between gravity and curvature? Why exactly is time treated in a different manner than other spatial dimensions? Introduction to Lorentz Geometry: Curves and Surfaces intends to provide the reader with the minimum mathematical background needed to pursue these very interesting questions, by presenting the classical theory of curves and surfaces in both Euclidean and Lorentzian ambient spaces simultaneously. Features: Over 300 exercises Suitable for senior undergraduates and graduates studying Mathematics and Physics Written in an accessible style without loss of precision or mathematical rigor Solution manual available on www.routledge.com/9780367468644 |
| Notes | Translated from the Portuguese. <P>1. Welcome to Lorentz-Minkowski Space. 1.1. Pseudo-Euclidean Spaces. 1.2. Subspaces of<STRONG> RQe</STRONG>. 1.3. Contextualization in Special Relativity. 1.4. Isometries in RQe. 1.5. Investigating O1(2, <B>R</B>) And O1(3, <B>R</B>). 1.6 Cross Product in <STRONG>RQe</STRONG>. 2. Local Theory of Curves. 2.1. Parametrized Curves in <STRONG>RQe</STRONG>. 2.2. Curves in the Plane. 2.3. Curves in Space. 3. Surfaces in Space. 3.1. Basic Topology of Surfaces. 3.2. Casual type of Surfaces, First Fundamental Form. 3.3. Second Fundamental Form and Curvatures. 3.4. The Diagonalization Problem. 3.5. Curves in Surface. 3.6. Geodesics, Variational Methods and Energy. 3.7. The Fundamental Theorem of Surfaces. 4. Abstract Surfaces and Further Topics. 4.1. Pseudo-Riemannian Metrics. 4.2. Riemann's Classification Theorem. 4.3. Split-Complex Numbers and Critical Surfaces. 4.4 Digression: Completeness and Causality</P> |
| Subject | GEOMETRY, DIFFERENTIAL. LORENTZ TRANSFORMATIONS. CURVES. SURFACES. MATHEMATICAL PHYSICS. MATHEMATICS / Arithmetic SCIENCE / Mathematical Physics MATHEMATICS / Geometry / General |
| Multimedia |