Intermediate turbine housing for a gas turbine, in particular an aircraft gas turbine, comprising a radial inner wall ; a radial outer wall ; the inner wall and the outer wall delimiting an annular space through which hot gas flows, and the inner wall and the outer wall each having contours which face the annular space and, relative to an axial longitudinal section through the intermediate turbine housing , describe an inner annular space curve along the inner wall and an outer annular space curve along the outer wall ; at least one blade element which extends through the annular space in the radial direction (RR) and has an axial leading edge and an axial trailing edge , the blade element having an outer axial width (AB) which is measured between the leading edge and the trailing edge and related to the outer wall and an inner axial width (IB) which is measured between the leading edge and the trailing edge and related to the inner wall , the outer annular space curve and/or the inner annular space curve having at least one curved portion which has a point of maximum gradient of the relevant annular space curve , the curved portion being located in the region of the leading edge or the trailing edge relative to the outer axial width (AB) and/or the inner axial width (IB), and the curved portion intersecting the penetration point of the leading edge or the trailing edge through the outer wall or the inner wall , characterized in that the curved portion has a length (KL) which is projected in parallel with the axial direction (AR) and is up to 20% of the relevant axial width (AB, IB), and the outer annular space curve has a turning point in the region of the leading edge and a turning point in the region of the trailing edge . a radial inner wall ; a radial outer wall ; the inner wall and the outer wall delimiting an annular space through which hot gas flows, and the inner wall and the outer wall each having contours which face the annular space and, relative to an axial longitudinal section through the intermediate turbine housing , describe an inner annular space curve along the inner wall and an outer annular space curve along the outer wall ; at least one blade element which extends through the annular space in the radial direction (RR) and has an axial leading edge and an axial trailing edge , the blade element having an outer axial width (AB) which is measured between the leading edge and the trailing edge and related to the outer wall and an inner axial width (IB) which is measured between the leading edge and the trailing edge and related to the inner wall , the outer annular space curve and/or the inner annular space curve having at least one curved portion which has a point of maximum gradient of the relevant annular space curve , the curved portion being located in the region of the leading edge or the trailing edge relative to the outer axial width (AB) and/or the inner axial width (IB), and the curved portion intersecting the penetration point of the leading edge or the trailing edge through the outer wall or the inner wall , characterized in that the curved portion has a length (KL) which is projected in parallel with the axial direction (AR) and is up to 20% of the relevant axial width (AB, IB), and the outer annular space curve has a turning point in the region of the leading edge and a turning point in the region of the trailing edge . <EOS>