Skip to main content
Thammasat University Digital Collections
Home
Browse All
Log in

Help

English
English
Deutsch
Español
Pirate English
한국어 Korean
Français
ไทย Thai
Search
Advanced Search
Find results with:
error div
Add another field
Search by date
Search by date:
from
after
before
on
from:
to
to:
Searching collections:
Ebook Collection
Add or remove collections
Home
Ebook Collection
Geometry of mobius transformations : elliptic, parabolic and hyperbolic actions of...
Reference URL
Share
Add tags
Comment
Rate
To link to this object, paste this link in email, IM or document
To embed this object, paste this HTML in website
Geometry of mobius transformations : elliptic, parabolic and hyperbolic actions of SL[symbol]([real number])
Download
small (250x250 max)
medium (500x500 max)
Large
Extra Large
large ( > 500x500)
Full Resolution
Print
There is no file associated with this item.
Description
Rating
Title
Geometry
of
mobius
transformations
:
elliptic
,
parabolic
and
hyperbolic
actions
of
SL[symbol]([real
number])
Creator
Kisil, Vladimir V.
Contributors
World Scientific (Firm)
DescriptionAbstract
This
book
is
a
unique
exposition
of
rich
and
inspiring
geometries
associated
with
Mobius
transformations
of the
hypercomplex
plane
. The
presentation
is
selfcontained
and
based
on the
structural
properties
of the
group
SL[symbol](real
number)
.
Starting
from
elementary
facts
in
group
theory
, the
author
unveils
surprising
new
results
about
the
geometry
of
circles
,
parabolas
and
hyperbolas
,
using
an
approach
based
on the
Erlangen
programme
of
F
.
Klein
,
who
defined
geometry
as a
study
of
invariants
under
a
transitive
group
action
. The
treatment
of
elliptic
,
parabolic
and
hyperbolic
Mobius
transformations
is
provided
in a
uniform
way
. This
is
possible
due
to an
appropriate
usage
of
complex
,
dual
and
double
numbers
which
represent
all
nonisomorphic
commutative
associative
twodimensional
algebras
with
unit
. The
hypercomplex
numbers
are in
perfect
correspondence
with the
three
types
of
geometries
concerned
.
Furthermore
,
connections
with the
physics
of
Minkowski
and
Galilean
spacetime
are
considered
.
DescriptionTable Of Contents
1
.
Erlangen
programme
:
preview
.
1.1
.
Make
a
guess
in
three
attempts
.
1.2
.
Covariance
of
FSCc
.
1.3
.
Invariants
:
algebraic
and
geometric
.
1.4
.
Joint
invariants
:
orthogonality
.
1.5
.
Higherorder
joint
invariants
:
focal
orthogonality
.
1.6
.
Distance
,
length
and
perpendicularity
.
1.7
. The
Erlangen
programme
at
large

2
.
Groups
and
homogeneous
spaces
.
2.1
.
Groups
and
transformations
.
2.2
.
Subgroups
and
homogeneous
spaces
.
2.3
.
Differentiation
on
Lie
groups
and
Lie
algebras

3
.
Homogeneous
spaces
from the
group
SL[real
number]
.
3.1
. The
affine
group
and the
real
line
.
3.2
.
Onedimensional
subgroups
of
SL[real
number]
.
3.3
.
Twodimensional
homogeneous
spaces
.
3.4
.
Elliptic
,
parabolic
and
hyperbolic
cases
.
3.5
.
Orbits
of the
subgroup
actions
.
3.6
.
Unifying
EPH
cases
: the
first
attempt
.
3.7
.
Isotropy
subgroups

4
. The
extended
FillmoreSpringerCnops
construction
.
4.1
.
Invariance
of
cycles
.
4.2
.
Projective
spaces
of
cycles
.
4.3
.
Covariance
of
FSCc
.
4.4
.
Origins
of
FSCc
.
4.5
.
Projective
crossratio

5
.
Indefinite
product
space
of
cycles
.
5.1
.
Cycles
: an
appearance
and the
essence
.
5.2
.
Cycles
as
vectors
.
5.3
.
Invariant
cycle
product
.
5.4
.
Zeroradius
cycles
.
5.5
.
CauchySchwarz
inequality
and
tangent
cycles

6
.
Joint
invariants
of
cycles
:
orthogonality
.
6.1
.
Orthogonality
of
cycles
.
6.2
.
Orthogonality
miscellanea
.
6.3
.
Ghost
cycles
and
orthogonality
.
6.4
.
Actions
of
FSCc
matrices
.
6.5
.
Inversions
and
reflections
in
cycles
.
6.6
.
Higherorder
joint
invariants
:
focal
orthogonality

7
.
Metric
invariants
in
upper
halfplanes
.
7.1
.
Distances
.
7.2
.
Lengths
.
7.3
.
Conformal
properties
of
Mobius
maps
.
7.4
.
Perpendicularity
and
orthogonality
.
7.5
.
Infinitesimalradius
cycles
.
7.6
.
Infinitesimal
conformality

8
.
Global
geometry
of
upper
halfplanes
.
8.1
.
Compactification
of the
point
space
.
8.2
.
(Non)invariance
of the
upper
halfplane
.
8.3
.
Optics
and
mechanics
.
8.4
.
Relativity
of
spacetime

9
.
Invariant
metric
and
geodesics
.
9.1
.
Metrics
,
curves
'
lengths
and
extrema
.
9.2
.
Invariant
metric
.
9.3
.
Geodesics
:
additivity
of
metric
.
9.4
.
Geometric
invariants
.
9.5
.
Invariant
metric
and
crossratio

10
.
Conformal
unit
disk
.
10.1
.
Elliptic
Cayley
transforms
.
10.2
.
Hyperbolic
Cayley
transform
.
10.3
.
Parabolic
Cayley
transforms
.
10.4
.
Cayley
transforms
of
cycles

11
.
Unitary
rotations
.
11.1
.
Unitary
rotations

an
algebraic
approach
.
11.2
.
Unitary
rotations

a
geometrical
viewpoint
.
11.3
.
Rebuilding
algebraic
structures
from
geometry
.
11.4
.
Invariant
linear
algebra
.
11.5
.
Linearisation
of the
exotic
form
.
11.6
.
Conformality
and
geodesics
.
Publisher
Imperial College Press
Distributed by World Scientific Pub. Co.
Subject
Mobius transformations.
Identifier
9781848168596
(electronic
bk.)
;
1848168586
;
9781848168589
;
http://www.worldscientific.com/worldscibooks/10.1142/P835#t=toc
Language
eng
Type
Electronic books.
FormatExtent
xiv, 192 p. : ill.
Date
c2012
.
OCLC number
874497303
CONTENTdm number
238
Tags
Add tags
for Geometry of mobius transformations : elliptic, parabolic and hyperbolic actions of SL[symbol]([real number])
View as list

View as tag cloud

report abuse
Comments
Post a Comment
for
Geometry of mobius transformations : elliptic, parabolic and hyperbolic actions of SL[symbol]([real number])
Your rating was saved.
you wish to report:
Your comment:
Your Name:
...
Back to top
Select the collections to add or remove from your search
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
Select All Collections
E
Ebook Collection
EReference
ETDA Publications
I
ISEAS (Institute of Southeast Asian Studies)
R
Rare books
S
Somdet Phra Nyanasamvara
Special project (Bachelor of Arts Program in Journalism and Mass Communication)
T
Thailand Research Fund (TRF)
Thammasat History Collection
Thammasat University Research
Thammasat University Textbooks
Thammasat University Theses
The 2011 Flood at TU
The Foundation for the Promotion of Social Sciences and Humanities
The Thai Democratization Center
W
Wat Bowonniwet Vihara Cremation Collection
500
You have selected:
1
OK
Cancel