In[]:=
ellipsoid
SURFACE

Ricci tensor

Out[]=
In[]:=
%[a,b,c][u,v]
Out[]=
In[]:=
Tr[%]
Out[]=
2
Cos[v]
(
2
a
2
Cos[u]
+
2
b
2
Sin[u]
)+
2
c
2
Sin[v]
+(
2
b
2
Cos[u]
+
2
a
2
Sin[u]
)
2
Sin[v]
In[]:=
FullSimplify[%]
Out[]=
1
2
(
2
a
+
2
b
+
2
c
-(
2
c
+(-
2
a
+
2
b
)Cos[2u])Cos[2v])
In[]:=
%/.{ba,ca}
Out[]=
1
2
(3
2
a
-
2
a
Cos[2v])
In[]:=
ellipsoid
SURFACE
["Properties"]
Out[]=
In[]:=
EntityList["Surface"]
Out[]=
{}
In[]:=
ellipsoid
SURFACE
Out[]=
ellipsoid
In[]:=
InputForm[%]
Out[]//InputForm=
Entity[Surface, Ellipsoid]