Jensen G.R. — Higher Order Contact of Submanifolds of Homogeneous Spaces :: Электронная библиотека попечительского совета мехмата МГУ

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Jensen G.R. — Higher Order Contact of Submanifolds of Homogeneous Spaces

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Название: Higher Order Contact of Submanifolds of Homogeneous Spaces

Автор: Jensen G.R.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

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Год издания: 1977

Количество страниц: 154

Добавлена в каталог: 15.08.2008

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Предметный указатель

$h_{0} : G \to L (M)$       6
$h_{1} : G \times W_{1} \to L (M^{(1)})$       13
$h_{2} : G \times W_{2} \to L (M^{(2)})$       18
$L_{0}$       7
$L_{1}$       9
$L_{2}$       14
$L_{3}$       20
$\lambda_{0} : L_{0} \to G_{m_{0}, p}$       5 8
$\lambda_{1} : L_{1} \to G_{m_{1} + \mu_{1}, p}$       14
$\lambda_{2} : L_{2} \to G_{m_{2} + \mu_{2}, p}$       19
$\mathbb{C} G_{4, 2}$       81
$\mathbb{C} P^{2}$       67
$\mathbb{E} (3)$ (proper rigid motions)      45
$\mathbb{R}^{n \times p}$ , $\mathbb{R}^{n \times p^{*}}$       23
$\rho_{0} : G_{0} \to GL (m_{0}, \mathbb{R})$       6
$\rho_{1} : G_{1} \to GL (m_{1} + \mu_{1}; \mathbb{R})$       13
$\rho_{2} : G_{2} \to GL (m_{2} + \mu_{2}; \mathbb{R})$       19
$\tilde{G}_{4, 2}$       5
Adapted frames      6
Adjoint representation      7
Bundle map      6 13 18
Calabi's Theorem      79
Congruence, definition      5
Congruence, theorem in $C^{q + 1}$ case      31
Congruence, theorem in $C^{w}$ case      23
Congruence, theorem in Lie groups      30
Contact between graphs      2
Contact, definition      1
Contact, G-contact      5 10
Covariant derivative      27
Curves in $\tilde{G}_{4, 2} = \frac{SO (4)}{SO (2) \times SO (2)}$       58
Curves in $\tilde{G}_{4, 2} = \frac{SO (4)}{SO (2) \times SO (2)}$ , type Ia      60
Curves in $\tilde{G}_{4, 2} = \frac{SO (4)}{SO (2) \times SO (2)}$ , type IaIIa ("helix")      61
Curves in $\tilde{G}_{4, 2} = \frac{SO (4)}{SO (2) \times SO (2)}$ , type IaIIb ("helix")      62
Curves in $\tilde{G}_{4, 2} = \frac{SO (4)}{SO (2) \times SO (2)}$ , type Ib      62
Curves in $\tilde{G}_{4, 2} = \frac{SO (4)}{SO (2) \times SO (2)}$ , type Ic      63
Curves in $\tilde{G}_{4, 2} = \frac{SO (4)}{SO (2) \times SO (2)}$ , type IcIIa ("geodesic")      64
Curves in $\tilde{G}_{4, 2} = \frac{SO (4)}{SO (2) \times SO (2)}$ , type IcIIb ("helix")      64
Existence of submanifolds      30
Frame field      6
Frame field, first order      9
Frame field, second order      14
Frame field, third order      20
Frame field, zeroth order      7
Frenet frame      22
Gauss curvature      78
Grassmann bundle      5
Grassmann bundle of $\mathbb{R}^{n}$       3
Grassmann bundle, manifold      23 58
Holomorphic curves in $\mathbb{C} G_{4, 2}$       81
Holomorphic curves in $\mathbb{C} G_{4, 2}$ , type Ia      83
Holomorphic curves in $\mathbb{C} G_{4, 2}$ , type IaIIa (special ruled surface)      85
Holomorphic curves in $\mathbb{C} G_{4, 2}$ , type IaIIb      86
Holomorphic curves in $\mathbb{C} G_{4, 2}$ , type IaIIbIIIa (pencil)      88
Holomorphic curves in $\mathbb{C} G_{4, 2}$ , type IaIIbIIIb      91
Holomorphic curves in $\mathbb{C} G_{4, 2}$ , type IaIIc      93
Holomorphic curves in $\mathbb{C} G_{4, 2}$ , type IaIIcIIIa (homogeneous)      95
Holomorphic curves in $\mathbb{C} G_{4, 2}$ , type IaIIcIIIb      97
Holomorphic curves in $\mathbb{C} G_{4, 2}$ , type Ib (special ruled surface)      98
Holomorphic curves in $\mathbb{C} G_{4, 2}$ , type Ic      101

Holomorphic curves in $\mathbb{C} G_{4, 2}$ , type IcIIa (special ruled surfaces)      103
Holomorphic curves in $\mathbb{C} G_{4, 2}$ , type IcIIb (homogeneous)      106
Holomorphic curves in $\mathbb{C} G_{4, 2}$ , type IcIIc      110
Holomorphic curves in $\mathbb{C} G_{4, 2}$ , type IcIId      113
Holomorphic curves in $\mathbb{C} P^{2}$       66
Holomorphic curves in $\mathbb{C} P^{2}$ , type IIa (hyperplane)      71
Holomorphic curves in $\mathbb{C} P^{2}$ , type IIb      71
Holomorphic curves in $\mathbb{C} P^{2}$ , type IIbIIIa (Veronese variety)      73
Holomorphic curves in $\mathbb{C} P^{2}$ , type IIbIIIb      74
Holomorphic curves in $\mathbb{C} P^{2}$ , type IIbIIIbi (generic)      76
Holomorphic curves in $\mathbb{C} P^{2}$ , type IIbIIIbii (W-curves)      76
Homogeneous submanifolds      41
Invariants in terms of Maurer — Cartan form      25
Invariants, constant      42
Invariants, first order      10
Invariants, second order      14
Invariants, third order      20
Isotropy subgroup      6
Linear isotropy representation      6
Local cross section      8 14
Maurer — Cartan equations      23
Maurer — Cartan form      23
Orientation of frames      7 10 15
Pick invariant      143 147
Projections $\psi_{1} : G_{m_{1} + \mu_{1}; p} \to G_{m_{0}, p}$       14
Projections $\psi_{2} : G_{m_{2} + \mu_{2}; p} \to G_{m_{1} + \mu_{1}; p}$       19
Relations among invariants      26
SO (4), Su (3), SU (4)      81
Special affine group $SL (3; \mathbb{R}) \cdot \mathbb{R}^{3}$       116
Special affine surface theory      115
Special affine surface theory, type IIa (planar)      120
Special affine surface theory, type IIb (parabolic)      120
Special affine surface theory, type IIbIIa      122
Special affine surface theory, type IIbIIIaIVa (cylinder $z = \frac{1}{2} x^{2}$ )      124
Special affine surface theory, type IIbIIIaIVb      124
Special affine surface theory, type IIbIIIaIVbi (homogeneous cylinder)      126
Special affine surface theory, type IIbIIIaIVbii (nonhomogeneous cylinders)      127
Special affine surface theory, type IIbIIIb      129
Special affine surface theory, type IIbIIIbVa      133
Special affine surface theory, type IIbIIIbVaVIa (homogeneous cone)      134
Special affine surface theory, type IIbIIIbVaVIb      136
Special affine surface theory, type IIbIIIbVb      138
Special affine surface theory, type IIc (elliptic)      139
Special affine surface theory, type IIcIIIa (homogeneous quadric)      143
Special affine surface theory, type IIcIIIb      146
Special affine surface theory, type IIcIIIbIVa (group manifold)      148
Special affine surface theory, type IIcIIIbIVb      149
Special ruled surfaces in $\mathbb{C} P^{3}$       85f 98—100 103—106
Structure equations of f      40
Surfaces in Euclidean Space      44
Surfaces in Euclidean space, type IIa (plane)      49
Surfaces in Euclidean space, type IIb (spheres)      50
Surfaces in Euclidean space, type IIc (minimal surfaces)      51
Surfaces in Euclidean space, type IIcIIIiii and IIdIIIbiii (cylinders, surfaces of revolution, helicoids)      57
Surfaces in Euclidean space, type IId (generic)      52
Surfaces in Euclidean space, type IIdIIIa (right circular cylinder)      55
Taylor polynomial      3 4
Type of a cross section      9 14 20
Type of a cross section, constant type      12 21
W-curves of Klein and Lie      76
Weingarten surfaces      57

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