Try giving your book type of any see if your data get assigned to book first:

book: any = [];

Also when you pushing data into book, try using this.book instead of passing the this into the function.

this.book.push({id:obj.id, title: obj.title, imagem: obj.imagem});

The problem was into my provider. Actually, it's kinda of a bug that I have to cast into just one object. My json was returning a Object Inside a object. I solved this problem by casting my res.json() into my object name: "book". Like this: res.json()['book']

    buscarLivro(id)
    {
      if (this.dataBook) 
      {
        return Promise.resolve(this.dataBook);
      }
      // Dont have the data yet
      return new Promise(resolve => {
        this.http.get('http://localhost:8000/api/books/'+id)
          .map(res => res.json()['book'])
          .subscribe((data: any) => {
            this.dataBook = data;
            resolve( this.dataBook);
          });
      });
    }