Dfyjkt

I want to have some text aligned to the center of the top or bottom of an ellipse. I've tried

documentclass[border=0.5]standalone
usepackage[utf8]inputenc
usepackage[T1]fontenc
usepackagemathtools,amsmath
usepackagetikz
usepackagepgfplots
pgfplotssetcompat=1.15

usetikzlibrarydecorations.text
begindocument
begintikzpicture
 draw (0,0) ellipse [x radius=3, y radius = 2];
 draw (0,0) ellipse [red,x radius=4, y radius = 2.66];
 draw(0,0) ++(-3.5,0) [decorate,decoration=text along path, text=This text should be between the eppelipses in the bottom half] arc [start angle=-160, end angle=-10, x radius=3.5, y radius = 3];
 draw(0,0) ++(-3.5,0) [decorate,decoration=text along path, text= This text should be centered and in the top half] arc [start angle=160, end angle=10, x radius=3.5, y radius = 4];
 node at (0,0) center text;
endtikzpicture
enddocument

I get

I guess you need to run the arc over the full length and also account for the height of the text. EDIT: Added text align=center, another big thanks to Max!

documentclass[border=0.5]standalone
usepackage[utf8]inputenc
usepackage[T1]fontenc
usepackagemathtools,amsmath
usepackagetikz

usetikzlibrarydecorations.text
begindocument
begintikzpicture
 draw (0,0) ellipse [x radius=3, y radius = 2];
 draw (0,0) ellipse [red,x radius=4, y radius = 2.66];
 pgfmathsetmacromyx(3.5cm+height("T")*0.5pt)*1pt/1cm
 pgfmathsetmacromyy(2.33cm+height("T")*0.5pt)*1pt/1cm
 draw [decorate,decoration=text along path,text align=center,
 text=This text should be between the ellipses in the bottom half] 
 (-myx,0) arc [start angle=-180, end angle=00, x radius=myx, y radius = myy];
 pgfmathsetmacromyx(3.5cm-height("T")*0.5pt)*1pt/1cm
 pgfmathsetmacromyy(2.33cm-height("T")*0.5pt)*1pt/1cm
 draw [decorate,decoration=text along path,text align=center,
 text= This text
 should be centered and in the top half] 
 (180:myx and myy) arc [start angle=180,
 end angle=0, x radius=myx, y radius = myy];
 node at (0,0) center text;
endtikzpicture
enddocument