Riemannscher Krümmungstensor - Versionsgeschichte

*>SchuBot: Einrückungen Mathematik

2010-09-12T17:29:46Z

Einrückungen Mathematik

← Nächstältere Version		Version vom 12. September 2010, 19:29 Uhr
Zeile 15:		Zeile 15:

	== Herleitung ==		== Herleitung ==
	<math>		:<math>
	{A^{\color{Violet}\alpha}}_{;{\color{Orange}\mu} {\color{Red}\nu}}		{A^{\color{Violet}\alpha}}_{;{\color{Orange}\mu} {\color{Red}\nu}}
	-		-
Zeile 50:		Zeile 50:

	=== Bianchi Identität ===		=== Bianchi Identität ===
	<math>{R^{{\color{Violet}\alpha} {\color{WildStrawberry}\beta}}}_{< {\color{Orange}\mu} {\color{Red}\nu};\sigma>}		:<math>{R^{{\color{Violet}\alpha} {\color{WildStrawberry}\beta}}}_{< {\color{Orange}\mu} {\color{Red}\nu};\sigma>}
	=		=
	{R^{{\color{Violet}\alpha} {\color{WildStrawberry}\beta}}}_{{\color{Orange}\mu} {\color{Red}\nu};\sigma}		{R^{{\color{Violet}\alpha} {\color{WildStrawberry}\beta}}}_{{\color{Orange}\mu} {\color{Red}\nu};\sigma}

2009-04-09T12:58:02Z

Bianchi Identität

← Nächstältere Version		Version vom 9. April 2009, 14:58 Uhr
Zeile 50:		Zeile 50:

	=== Bianchi Identität ===		=== Bianchi Identität ===
	<math>{R^{{\color{Violet}\alpha} {\color{WildStrawberry}\beta}}_{< {\color{Orange}\mu} {\color{Red}\nu};\sigma>}		<math>{R^{{\color{Violet}\alpha} {\color{WildStrawberry}\beta}}}_{< {\color{Orange}\mu} {\color{Red}\nu};\sigma>}
	=		=
	~~<math>~~{R^{{\color{Violet}\alpha} {\color{WildStrawberry}\beta}}_{{\color{Orange}\mu} {\color{Red}\nu};\sigma}		{R^{{\color{Violet}\alpha} {\color{WildStrawberry}\beta}}}_{{\color{Orange}\mu} {\color{Red}\nu};\sigma}
	+		+
	~~<math>~~{R^{{\color{Violet}\alpha} {\color{WildStrawberry}\beta}}_{\sigma {\color{Orange}\mu}; {\color{Red}\nu}}		{R^{{\color{Violet}\alpha} {\color{WildStrawberry}\beta}}}_{\sigma {\color{Orange}\mu}; {\color{Red}\nu}}
	+		+
	~~<math>~~{R^{{\color{Violet}\alpha} {\color{WildStrawberry}\beta}}_{{\color{Red}\nu} \sigma ;{\color{Orange}\mu} }		{R^{{\color{Violet}\alpha} {\color{WildStrawberry}\beta}}}_{{\color{Red}\nu} \sigma ;{\color{Orange}\mu} }
	=0		=0
	</math>		</math>

	[[Kategorie:Tensor 4. Stufe]]		[[Kategorie:Tensor 4. Stufe]]

2009-04-09T12:56:14Z

Symmetrien

@@ Zeile 46: / Zeile 46: @@
++
 {R^{\color{Violet}\alpha}}_{ {\color{Red}\nu}{\color{WildStrawberry}\beta} {\color{Orange}\mu} }
 </math>
 [[Kategorie:Tensor 4. Stufe]]

2009-04-09T12:52:43Z

Symmetrien

@@ Zeile 26: / Zeile 26: @@
 == Symmetrien ==
-<math>R_{{\color{Violet}\alpha}{\color{WildStrawberry}\beta} {\color{Orange}\mu} {\color{Red}\nu}}
+ * <math>
+=
-R_{{\color{Orange}\mu} {\color{Red}\nu} {\color{Violet}\alpha}{\color{WildStrawberry}\beta} }</math>
+R_{{\color{Orange}\mu} {\color{Red}\nu} {\color{Violet}\alpha}{\color{WildStrawberry}\beta} }
-[[Kategorie:Tensor_4._Stufe]]
+[[Kategorie:Tensor 4. Stufe]]

2009-04-09T12:48:08Z

← Nächstältere Version		Version vom 9. April 2009, 14:48 Uhr
Zeile 25:		Zeile 25:
	</math>		</math>

	[[Kategorie:~~Tensor 4~~. ~~Stufe~~]]		== Symmetrien ==
			<math>R_{{\color{Violet}\alpha}{\color{WildStrawberry}\beta} {\color{Orange}\mu} {\color{Red}\nu}}
			=
			R_{{\color{Orange}\mu} {\color{Red}\nu} {\color{Violet}\alpha}{\color{WildStrawberry}\beta} }</math>

			[[Kategorie:Tensor_4._Stufe]]

2009-04-09T12:45:46Z

Herleitung

← Nächstältere Version		Version vom 9. April 2009, 14:45 Uhr
Zeile 21:		Zeile 21:
	=		=
	{R^{\color{Violet}\alpha}} _{{\color{WildStrawberry}\beta} {\color{Orange}\mu} {\color{Red}\nu}}		{R^{\color{Violet}\alpha}} _{{\color{WildStrawberry}\beta} {\color{Orange}\mu} {\color{Red}\nu}}
	{A^{\color{~~Violet~~}\beta}}		{A^{\color{WildStrawberry}\beta}}

	</math>		</math>

	[[Kategorie:Tensor 4. Stufe]]		[[Kategorie:Tensor 4. Stufe]]

2009-04-09T12:45:11Z

Herleitung

← Nächstältere Version		Version vom 9. April 2009, 14:45 Uhr
Zeile 20:		Zeile 20:
	{A^{\color{Violet}\alpha}}_{;{\color{Red}\nu} {\color{Orange}\mu}}		{A^{\color{Violet}\alpha}}_{;{\color{Red}\nu} {\color{Orange}\mu}}
	=		=
	{R^{\color{Violet}\alpha}} _		{R^{\color{Violet}\alpha}} _{{\color{WildStrawberry}\beta} {\color{Orange}\mu} {\color{Red}\nu}}
	{{\color{WildStrawberry}\beta} {\color{Orange}\mu} {\color{Red}\nu}}</math>		{A^{\color{Violet}\beta}}

			</math>

	[[Kategorie:Tensor 4. Stufe]]		[[Kategorie:Tensor 4. Stufe]]

2009-04-09T12:44:33Z

Herleitung

← Nächstältere Version		Version vom 9. April 2009, 14:44 Uhr
Zeile 15:		Zeile 15:

	== Herleitung ==		== Herleitung ==
	<math>{A^{\color{Violet}\alpha}}}_{;{\color{Orange}\mu} {\color{Red}\nu}}		<math>
			{A^{\color{Violet}\alpha}}_{;{\color{Orange}\mu} {\color{Red}\nu}}
	-		-
	{A^{\color{Violet}\alpha}}}_{;{\color{Red}\nu} {\color{Orange}\mu}}		{A^{\color{Violet}\alpha}}_{;{\color{Red}\nu} {\color{Orange}\mu}}
	=		=
	{R^{\color{Violet}\alpha}} _		{R^{\color{Violet}\alpha}} _

2009-04-09T12:43:57Z

Herleitung

← Nächstältere Version		Version vom 9. April 2009, 14:43 Uhr
Zeile 15:		Zeile 15:

	== Herleitung ==		== Herleitung ==
	{A^{\color{Violet}\alpha}}}_{;{\color{Orange}\mu} {\color{Red}\nu}}		<math>{A^{\color{Violet}\alpha}}}_{;{\color{Orange}\mu} {\color{Red}\nu}}
	-		-
	{A^{\color{Violet}\alpha}}}_{;{\color{Red}\nu} {\color{Orange}\mu}}		{A^{\color{Violet}\alpha}}}_{;{\color{Red}\nu} {\color{Orange}\mu}}
	=		=
	{R^{\color{Violet}\alpha}} _		{R^{\color{Violet}\alpha}} _
	{{\color{WildStrawberry}\beta} {\color{Orange}\mu} {\color{Red}\nu}}		{{\color{WildStrawberry}\beta} {\color{Orange}\mu} {\color{Red}\nu}}</math>

	[[Kategorie:~~Tensor_4~~.~~_Stufe~~]]		[[Kategorie:Tensor 4. Stufe]]

2009-04-09T12:43:43Z

← Nächstältere Version		Version vom 9. April 2009, 14:43 Uhr
Zeile 13:		Zeile 13:
	\Gamma _{\sigma {\color{Orange}\mu} } ^ {\color{Violet}\alpha}		\Gamma _{\sigma {\color{Orange}\mu} } ^ {\color{Violet}\alpha}
	</math>		</math>

			== Herleitung ==
			{A^{\color{Violet}\alpha}}}_{;{\color{Orange}\mu} {\color{Red}\nu}}
			-
			{A^{\color{Violet}\alpha}}}_{;{\color{Red}\nu} {\color{Orange}\mu}}
			=
			{R^{\color{Violet}\alpha}} _
			{{\color{WildStrawberry}\beta} {\color{Orange}\mu} {\color{Red}\nu}}

	[[Kategorie:Tensor_4._Stufe]]		[[Kategorie:Tensor_4._Stufe]]