The phrase "manifests in the form" is correct and can be used in written English.
It is often used to describe how something (such as an idea or concept) becomes visible or apparent in a particular form or expression. Example: The artist's emotional turmoil manifests in the form of intense brushstrokes and vibrant colors in her paintings.
That reputation manifests in the form of crowdsourced investigations into Kennedy's past, such as his entry in Encyclopedia Dramatica (essentially, Wikipedia for 4Chan), which documents everything from allegations of "stealing linen" at an anime convention in 2005 to his failed web-hosting venture Flirble.me in 2013.
Fatigue damage manifests in the form of surface roughness change.
Aerodynamic resistance manifests in the form of single scaling factors with the dimensions of pressure gradients.
Double diffusive convection manifests in the form of "salt-fingers" (see Stern [2, 3]) which are observable in laboratory settings.
This variant is being increasingly recognized and manifests in the form of periportal soft-tissue cuffing or ill-defined mass [46, 47, 48].
SCA6 is caused by a CAG expansion in the CACNA1A gene and generally manifests in the form of pure ataxia [1 3].
Mr. Mfume said it was a reminder that intolerance was still manifest in the form of militia groups and anti-immigrant sentiment.
He came under increasing criticism from Madagascar's powerful Council of Malagasy Churches, and opposition among the capital's youth manifested in the form of participation in kung fu clubs.
It's important to remember that the brittle, nervous delicacy with which Muslims are regarded by both liberals and the establishment has an underside of tacit contempt, occasionally manifested in the form of intemperate outbursts about the "backwardness" of Islam.
Periodically, religious unrest was manifested in the form of political insurrections, especially in those exceptional times when a governor openly discriminated against the Copts by forcing them to wear distinctive clothing or, worse, by destroying their icons.
It can be manifested in the form of complex networks.
