444 10 Conclusion of Volume 2

Now I evaluate the curvature 2-form of your space

I find the following answer

R[12] =	e1	**e2s1 [t]
		s1[t]
R[13] =	e1	**e3s2 [t]
		s2[t]
R[14] =	e1	**e4s3 [t]
		s3[t]
R[23] =	e2	**e3s1[t]s2[t]
		s1[t]s2[t]
R[24] =	e2	**e4s1[t]s3[t]
		s1[t]s3[t]
R[34] =	e3	**e4s2[t]s3[t]
		s2[t]s3[t]

The result is encoded in a tensor RR[i,j]

Its components are encoded in a tensor Rie[i,j,a,b]

————————————-

Now I calculate the Ricci tensor 11 non-zero

22 non-zero

33 non-zero

44 non-zero

I have finished the calculation

The tensor ricten[a,b]] giving the Ricci tensor is ready for storing on hard disk

We display the Ricci tensor

ricten

s2 [t]

s3 [t]

((

1

2

s1 [t]

)

3

2

2

s1

[t

]

+ s2[t]

+ s3

[t] ,

0, 0,

0 ,

[

]

, 0, 0 ,

0,

s

[

]

s

1

[

]

s

3

[

]+

s

[

]

(s

1

[

]

s

2

[ ]+

s

[

]

s

1

t

)

(

t

t

t

[

t

t

t

t

)

s1

t s t s t

s3

t (s

t s

t

s1 t s t )

2s1

t

]s2[t

]s3[t

]

0, 0,

[ ] 2[ ] 3[ ]+ [ ] 1[ ] 2[ ]+ [ ] 2 [ ]

, 0 ,

(

s1 t s t s

t

[

s2

t (s

t s

t

s1 t s t ) )

2s1

t]s2

[t

]s3

[t

]

3[ ]+ [ ] 3 [ ]

(0, 0, 0,

[ ]

2

[ ]

3

[

]+ [ ]

1[ ]

))

2s1[t]s2[t]s3[t]

The above result presents the Ricci tensor for a Kasner like metric with three independent scale factors for each of the three Euclidian axes.

References

1.Frè, P., Grassi, P.A.: Pure spinor formalism for Osp(N |4) backgrounds. arXiv:0807.0044 [hepth]